Experiment 14: Refractive Index of Glass Slab PDF

EXPERIMENT 14 AIM To determine refractive index of a glass slab using a travelling microscope. APPARATUS AND MATERIAL REQUIRED A travelling microscope, a glass slab, lycopodium powder/chalk dust and a paper. Fig. E 14.1 Formation of ima...

EXPERIMENT 14 AIM To determine refractive index of a glass slab using a travelling microscope. APPARATUS AND MATERIAL REQUIRED A travelling microscope, a glass slab, lycopodium powder/chalk dust and a paper. Fig. E 14.1 Formation of image I of a point 0 in a glass slab PRINCIPLE If a glass slab is placed in air on a horizontal surface and its bottom surface is viewed from top, it appears to be elevated due to the phenomenon of refraction. The distance between this apparent bottom and the top surface of the slab gives the apparent thickness of the slab. In case of normal observation, it can be shown that the refractive index of glass with respect to the medium, air is, real thickness of the slab n ga = apparent thickness of the slab 24/04/2018 LABORATORY MANUAL P ROCEDURE 1. Find the least count of the microscope scale, being used. 2. Put a mark on a sheet of paper. 3. Place the paper on the horizontal platform of the microscope. Adjust the microscope in such a way that its lens system is vertically above the mark. 4. Focus the microscope on the mark and record the reading a 1 using Main Scale Reading (MSR) and Vernier Scale Reading (VSR) of its coinciding division as shown in the Table E 14.1. 5. Next, place the glass slab over the mark on the sheet of paper. 6. Move the microscope upward until mark on the paper, seen through the slab is sharp and clear. Take the reading a2 with the main scale and coinciding division of the vernier scale. 7. Spread a little lycopodium powder/chalk dust over the top surface of the glass slab. 8. Raise the lens system of the microscope and focus the microscope to see some of their particles clearly and record reading a3. 9. Invert the slab and repeat steps 3 to 8. O BSERVATIONS Least Count (LC) of the travelling microscope: 20 Main Scale Divisions (MSD) = 1 cm (say) 1 ∴ 1 MSD = cm 20 50 Vernier Scale Divisions (VSD) = 49 MSD (say) 49 49 1 ∴ 1 VSD = MSD = × cm 50 50 20 Least Count of the microscope = (1 MSD – 1 VSD) ⎡ 1 − ⎛ 49 ⎞ × 1 ⎤ 1 ⎛1 − 49 ⎞ = ⎢⎣20 ⎜⎝ 50 ⎟⎠ 20⎥⎦ = 20 ⎜⎝ 50 ⎟⎠ cm LC = 0.001 cm 106 24/04/2018  E XPERIMENT 14 13 Table E 14.1: Refractive index of glass slab Reading of the microscope when focused on Sl. Mark Mark on paper Particles on no. made on paper through the slab top of the glass surface M.S.R. V.S.R. a1=M+ M.S.R. V.S.R. a2=M+ M.S.R. V.S.R. a3=M+ M N N× M N N× M N N× L.C. L.C. L.C. (cm) (cm) (cm) (cm) (cm) (cm) (cm) (cm) (cm) 1 2 3 C ALCULATIONS The refractive index n ga is given by real thickness of the slab a − a3 b n ga = = 1 = (say) apparent thickness of the slab a1 − a 2 c Find nga for the two sets of observations and then the mean value of nga. Error The estimated uncertainty in the measurement of n ga is ∆n ga ⎛ ∆b ∆c ⎞ n ga = ⎜ ⎝ b + c ⎠ ⎟ (E 14.1) ∆b  ∆a ∆a 3  (E 14.2) where =  1 +  b  a1 a3  ∆c  ∆a ∆a 2  (E 14.3) and =  1 +  c  a1 a2  From Eq. (E14.1) ∆n ga  2∆a 2 ∆a  =  +  n ga  b c   ∆a ∆a  or ∆n ga = 2n ga  +  b c  ∆a = least count of microscope and hence uncertainty in ai, a2, and a3 measurements. 107 24/04/2018 LABORATORY MANUAL Maximum value of ∆n ga as obtained from the two sets of observations should be reported with the result as experimental error. R ESULT The refractive index of glass of the slab was found to be nga ± ∆n ga=... ±... nga is mean value of refractive index of glass with respect to the medium air. P RECAUTIONS 1. The screws used in focussing the microscope should be moved in only one direction to avoid back-lash error. 2. Once the microscope is focused for the first reading i.e., a1, the focusing arrangement in the lens system should not be changed/altered for subsequent readings namely for a2 and a3. 3. The glass slab should be placed on a horizontal surface. 4. Use hand lens/magnifying glass to read the vernier scale to avoid error in finding vernier coinciding division. S OURCES OF ERROR 1. Position of the microscope may not be normal to the surface of the glass slab. 2. If the layer of lycopodium powder/chalk dust spread on the glass slab is thick, it will not actually represent the top of the glass slab and thus produce error in the result. D ISCUSSION 1. You will get a feel of the apparent and real depths if you try to lift a coin in a bucket filled with water. 2. Consider the situation in which rays coming from an object strike on the glass slab obliquely. Can you obtain a mathematical expression for n ga? S ELF ASSESSMENT 1. Will a colourless slab be visible if immersed in a transparent liquid of the same refractive index as that of the slab? State the reason for it. 108 24/04/2018  E XPERIMENT 14 13 2. You have three slabs of same dimensions – the first one being hollow and completely filled with water, the second one is made of crown glass and the third flint glass. If each of them has a coloured mark at the bottom, in which case will it appear to have risen the most? Given its n flint > n crown > n water SUGGESTED ADDITIONAL EXPERIMENTS/ACTIVITIES Use the method mentioned above to find the refractive indices of commonly available transparent liquids. You may use a thin glass beaker for this experiment. 109 24/04/2018 LABORATORY MANUAL EXPERIMENT 15 AIM To determine the refractive index of a liquid (water) using (i) concave mirror, (ii) convex lens and a plane mirror. (i) Refractive index of water using concave mirror APPARATUS AND MATERIAL REQUIRED Concave mirror of small aperture and large focal length, water, a laboratory stand with rigid base and clamp arrangement (height of the stand must be more than double the focal length of the given concave mirror), a pin, a metre scale, a spirit level, a plumb line, and some small cork pieces. PRINCIPLE When an object is placed in front of the reflecting surface of a concave mirror MM′ at a distance equal to its radius of curvature R, a real and inverted image is formed at the centre of curvature, i.e., u = v = R = distance PC; P being the pole of the mirror [Fig. E15.1 (a)]. Thus the centre of curvature C of a concave mirror Fig. E 15.1 Formation of image A′B′ of an object AB by a concave mirror MM′ placed at its centre of curvature. (a) Mirror without water and can be located by (b) Mirror with some water the method of 110 parallax between 24/04/2018  E XPERIMENT 15 13 a sharp-edged pin and its real and inverted image formed by a concave mirror. Fig. E 15.1(b) shows the location of centre of curvature C′ when the mirror is partially filled with some transparent liquid (say water). In this case the parallax between the object pin and image of the pin would be removed at a shorter distance from the pole P of the mirror. The incident ray C′N is refracted at the water -air boundary along the path NM such that it falls normally on the curved reflecting surface at point M. The reflected ray retraces back on the same path along MN in water and meets the axis at C along NC, when produced. In air, actually the reflected ray travels along NC′. Thus the real and inverted image is formed at C′. Therefore the distance PC′ would be the apparent radius of curvature R′ of the water-filled concave mirror. Fig. E 15.1(b) shows the refraction of incident ray C′N in water. Let ZZ′ be the normal at the water surface. ∠ZNC′ and ∠ZNC are the angles of incidence i and refraction r, respectively. From geometrical arguments, it is clear that ∠i = ∠NC′P and ∠r = ∠NCP. Thus, the refractive index of water with respect to air n wa can be given as: NP' sin i NC' = NC n wa = = sin r NP' NC' NC For a mirror having very small aperture and large radius of curvature, distances NC and NC′ can be approximated as distances PC and P′C′, respectively. Further, if only a little quantity of water is taken in the mirror, then distance PP′ can be neglected in comparison to PC or PC′. Thus PC R n wa = = PC' R ' Thus, using this method the refractive index of any transparent liquid can be determined. P ROCEDURE 1. Obtain approximate value of focal length of the concave mirror by focussing the image of a distant object. It can be found by obtaining a sharp image of the Sun or a tree on a plane wall or on a sheet of paper, and measuring the distance between the mirror and image with a scale. This distance is an approximate value of the focal length f, of the concave mirror. Twice of this focal length is an approximate value of the radius of curvature of the mirror. 111 24/04/2018 LABORATORY MANUAL Note: Do not look at the Sun’s image in a concave mirror as it may hurt your eyes. 2. Place the given concave mirror on the base of a firm and stable laboratory stand keeping its reflecting surface upwards. Use a spirit level to ensure that the plane on which the mirror rests is horizontal. It makes the principal axis of the mirror vertical. Some pieces of paper, plasticine or cork may be used to keep the position of mirror stable on the stand. 3. Fix a sharp edged bright pin in the clamp and place it horizontally just above the mirror. Adjust the position of the pin such that its tip B lies just above the pole P of the mirror or lies on the principal axis of the mirror. 4. Shift the clamped pin to a distance roughly equal to twice the rough focal length of the concave mirror (obtained in step 1) from the pole P of the mirror placed on the laboratory stand. Once again verify that the tip of the pin and pole P lie along the same vertical line (principal axis of the mirror). 5. Adjust the position of the pin till the parallax between the tip of the pin and its inverted image is removed. 6. Measure the vertical distance between the tip of the pin and the mirror using a plumb line and metre scale. This distance would be the real radius of curvature of the mirror. 7. Pour some water on the curved surface of the mirror. 8. Lower the pin slowly, till once again the parallax between the tip of the pin and its inverted image formed by the water-filled mirror is removed. 9. Remove water from the mirror and measure the vertical distance between the tip of the pin and the mirror. This distance would be the apparent radius of curvature of the water-filled mirror. 10. Repeat the experiment (steps 2 to 9) atleast two more times. O BSERVATIONS 1. Approximate value of the focal length of the concave mirror, f =... cm. 2. Approximate value of the radius of curvature, R = 2f =... cm. 112 24/04/2018  E XPERIMENT 15 13 Table E 15.1: Observations for R, R′ and nwa Sl. No. Position of pin with respect to pole P nwa= ∆n wa R/R ′ For empty concave For water - filled mirror, distance PC mirror, distance PC′ R (cm) R ′ (cm) 1 2 3 Mean C ALCULATIONS Calculate n wa and its mean value. Error ∆nwa ∆R ∆R' = + nwa R R' ⎡ ∆R ∆R ' ⎤ ∴ ∆n wa = ⎢ + n wa ⎣ R R ' ⎥⎦ R ESULT The refractive index of water with respect to air is nwa ± ∆nwa =.... ±.... nwa is mean value and ∆nwa is the maximum of the three values of error. P RECAUTIONS 1. Pin should be kept horizontal and above the curved reflecting surface of the horizontally placed concave mirror such that the tip of the pin lies above the pole of the mirror on its vertical principal axis. 2. Aperture of mirror should be small. 3. The mirror should be very thin otherwise multiple reflections will form an unclear image. 4. The quantity of water taken in the mirror should be sufficient so that the water surface remains horizontal, or else the surface may not remain horizontal because of surface tension. 5. Eye should be kept at a distance of more than 25 cm from the pin. 113 24/04/2018 LABORATORY MANUAL S OURCES OF ERROR The line joining PC may not be vertical. D ISCUSSION 1. If the refractive index of water is determined using concave mirrors of different radii of curvature, how will this affect the values of the refractive index? 2. A plumb line may be used to find the accurate value of PC and PC′. How can plumb line ensure correct measurement? S ELF ASSESSMENT 1. Find the refractive index of water from this experiment considering that a concave mirror filled with water behaves as a combination of concave mirror and a plano-convex lens. 2. If you gradually increase the quantity of water in the mirror, starting with a few drops, do you expect any change in the position or brightness of the image? 3. If colours are added to water keeping its transparency, would this alter the value of refractive index and intensity of the image? 4. If a small quantity of some transparent liquid (like kerosene) lighter than water is added such that it forms a thin film on the water surface; can the experiment still be performed? If so, would the value of refractive index change? SUGGESTED ADDITIONAL EXPERIMENTS/ACTIVITIES 1. Determine the refractive indices of different liquids (white vinegar, kerosene, glycerine, cooking oil). 2. Take a table lamp. Covering it with cellophane paper of various colours, determine the refractive index of a liquid (say, water) using a concave mirror. Do you observe any change in the value of refractive index of the liquid? 3. Study the variation in the refractive index of salt/sugar solution by changing its concentration. 114 24/04/2018  E XPERIMENT 15 13 (ii) Refractive index of water using convex lens and a plane mirror APPARATUS AND MATERIAL REQUIRED Double convex lens (focal length nearly 20 cm), plane mirror (bigger in size than the aperture of the lens), laboratory stand fixed with a pin in clamp, metre scale, plumb line, water dropper. PRINCIPLE In this method, a real and inverted image coincides with the object placed on the principal focus point of a convex lens. The rays from a pin AB placed on the principal focus F of a convex lens emerges out parallel to its axis. When these rays fall normally on a plane mirror placed horizontally below the convex lens, they retrace their path and form a real and inverted image A′ B′ at the principal focal plane of the lens [Fig. E 15.2(a)]. The size of image A′ B′ is equal to the size of object pin AB and the tip of the pin gives the position of the second principal focus. Then f (OF) is the focal length of the convex lens (for a thin lens) where O is the optical centre of the lens. F A' B' B A OF = f O Plane mirror (a) Fig. E 15.2 Image formed by a equiconvex lens backed by a plane mirror coinciding with the object AB. (a) A′ B′ when there is air in between the lens and the mirror; and (b) A″ B″ when there is water in between the lens and mirror Now, if the space between the lens and the plane mirror is filled with a transparent liquid (say water) having refractive index n wa, and the above procedure is repeated to find the position of the principal focus F in the new situation then the distance between the optical centre O 115 24/04/2018 LABORATORY MANUAL of the lens and point F′, OF′ (say f ′) would be the focal length of the combination of the two lenses. The combination consists of a glass convex lens (radius of curvature of both the curved surfaces are same, R and a water plano-concave lens of same radius of curvature, R. The focal length fw of water lens can be determined from the relation between the three focal lengths. viz. f′, f, and fw, i.e., (E 15.1) 1 1 1 = + f′ f fw 1 f – f′ (E 15.2) = fw f f′ But with sign convention : f = + ve, f ′ = + ve one finds fw = – ve f f′ fw = f − f′ Also, from the lens maker’s formula for a plano-concave lens 1 1 (E 15.3) = (n wa − 1) fw R f f′ Thus, R = (n wa − 1) f − f′ Hence,  R  (E 15.4) n wa = 1 +   fw  Following the procedure given in the Labratory Manual of Physics Class XI, (NCERT) Experiment-3, the radius of curvature R of the spherical surfaces of the convex lens (using a spherometer) can be determined, and Eq. 15.4 can be utilised for calculating n wa. Therefore, by using this method, the refractive index of a transparent liquid can be determined. P ROCEDURE 1. Place the plane mirror on the base of a rigid laboratory stand keeping its reflecting surface upwards. 2. Place the convex lens on the plane mirror. 3. Fix a sharp-edged bright pin in the clamp and place it horizontally and above the lens. Adjust the position of the pin such that its tip B lies vertically above the optical centre of the convex lens. A plumb line and a spirit level may be used to achieve this. 116 24/04/2018  E XPERIMENT 15 13 4. Shift the clamped pin gradually upward looking at the image and bring it to a height such that the tip B of the pin exactly coincides with the tip of its image B′. Ensure that there is no parallax between the object pin and its image. Measure the distance OF [Fig. E 15.2(a)]. For this, observe the distances of the pin from the upper and lower surfaces of the lens and take OF = f as the average of these two distances. 5. With the help of a dropper, put a few drops of water under the lens so that the space between mirror and lens is filled with water. 6. Move the object pin upward and remove the parallax between the tip of the object pin and its image for med by the lens mirror system. Measure the distance OF′ [Fig. E 15.2(b)]. Here again, as before, measure the distances of the pin from the two surfaces of the lens and take OF′ = f ′ as their average. 7. Repeat the experiment and record your observations in Table 15.2. O BSERVATIONS 1. Mean value of distance between the two legs of the spherometer l =...cm 2. Mean value of sagitta (bulge of the lens) h =...cm 3. Mean value of the radius of curvature of the lens R =...cm Table15.2 : Focal length of convex lens, OF (= f ) and water plano-convex lens OF′′ (= f ′ ) Sl. Position of pin with respect to optical centre f f′ ∆ fw n wa ∆n wa fw = No. O f – f′ Without water (OF =f ) With water (OF′ =f′ ) Distance of the pin from Distance of the pin from Upper Plane d + d Upper Plane d + d 1 2 3 4 surface mirror surface mirror of the 2 of the 2 lens lens d1 (cm) d2 (cm) f (cm) d3 (cm) d4 (cm) f′ (cm) 1 2 3 Mean 117 24/04/2018 LABORATORY MANUAL C ALCULATIONS ⎛ R⎞ n wa = ⎜1 + ⎝ ⎟ f w⎠ Error ∆n wa ∆R ∆f w = + nwa R fw ∆R ∆f w ⎤ or ∆nwa = nwa ⎡⎢ + ⎣ R f w ⎥⎦ *  2 ∆l 2 ∆h  where ∆R = R  +  l h  We use Eq. 15.1 for finding the value of ∆fw. ∆f w ∆f ∆f ′ 2 = 2 + 2 f w f f′ 2 ∆f ∆f ′ or, ∆f w = f w 2 + 2 f f′ Note that ∆l, ∆h, ∆f and ∆f′ represent least count of the measuring scale. R ESULT The refractive index of a given liquid (say water) with respect to air is n wa + ∆nwa =...±.... Here, nwa is mean value and ∆n wa is the maximum of three values of error. P RECAUTIONS 1. Pin should be kept horizontal and its tip should be above the optical centre of the lens on its vertical principal axis otherwise it will be difficult to remove the parallax. 2. The thin lens should be used so that the distance measured from its surface is nearly equal to the distance measured from the 118 * Please refer Laboratory Manual Class XI (NCERT) Experiment-3. 24/04/2018  E XPERIMENT 15 13 optical centre. Still it is better to measure distance from both the surfaces and take the average for f or f ′. 3. Water should be gently put between the mirror and the lens surface with the help of a dropper so that it may fill up the air space between them without disturbing the position of the lens. S OURCES OF ERROR 1. Two surfaces of the convex lens may not have the same radius of curvature. 2. The plane mirror may not be horizontal. D ISCUSSION 1. Convex lens used should be thin. How will the result change if a thick lens is used? 2. How is a plumb line effective in ensuring that the rays retrace their path after refraction through the lens and reflection from the mirror? Draw suitable diagram with principal axis at an angle to the vertical, showing the plane mirror at an angle to the horizontal. S ELF ASSESSMENT 1. What will happen if you are given a convex lens of small focal length? 2. What are the basic assumptions you have made in performing this experiment? 3. Why do we have to raise the object pin upward after filling water between the lens and the mirror? SUGGESTED ADDITIONAL EXPERIMENTS/ACTIVITIES 1. Find out refractive index of any other transparent liquid using this method. 2. Study the effect of change in concentration of a solution taken in between the lens and mirror on the refractive index of the solution. 3. Measure the focal length of the given convex lens using a plane mirror. Now replace the plane mirror with a convex mirror of the same curvature, and repeat the experiment to find the focal length of the lens. Draw a suitable ray diagram. 119 24/04/2018 LABORATORY MANUAL EXPERIMENT 16 AIM To draw the I - V characteristic curves of a p-n junction in forward bias and reverse bias. APPARATUS AND MATERIAL REQUIRED A p-n junction diode (OA-79 or 1N4007), a resistor of value (3Ω, 1/2W), one variable voltage power supply (0-12V), voltmeter (0-12V), milliammeter (0-200 mA), a plug key, connecting wires, sand paper and a microammeter (0-200 µA). T ERMS AND DEFINITIONS 1. Forward bias: When an external voltage is applied to a p-n junction diode in such a way that the p-side is at a higher potential with respect to the n-side, it is said to be forward biased. 2. Threshold voltage or “Cut-in” voltage: When the p-side is connected to the positive terminal of the battery and the voltage is increased, initially a negligible current flows till the applied voltage crosses a certain value. After, a characteristic voltage, the diode current increases significantly (exponentially), even for a very small increase in the diode bias voltage. This voltage is called the threshold voltage or cut-in-voltage of the diode. 3. Reverse bias: When the n-region of a p-n junction diode is at a higher potential with respect to the p-region, it is said to be reverse biased. In reverse bias, the p-side of the p-n junction diode is connected to the negative of the battery. 4. Reverse saturation current: As the applied voltage is increased in the reverse biased condition, starting from zero value, the current increases, but soon becomes constant. This current is very small (a few microamperes). It is called the reverse saturation current. 120 24/04/2018  E XPERIMENT 16 13 P ROCEDURE 1. Note the range and least count of the given voltmeter (V), milliammeter (mA) and the microammeter (µA). 2. Remove the insulating layers from the connecting wires and leads of diode using a sand paper. 3. Connect the variable voltage power supply, p-n junction diode, voltmeter, milliammeter, resistor and a plug key in a circuit as shown in Fig. E 16.1. 4. Initially when the key is open, you would note at this stage, that no current is flowing through the circuit. Now close the key. Fig. E 16.1 Forward biasing for a p-n junction diode 5. Give a small voltage to the circuit by slight and gentle turning of the power supply knob. Note the voltmeter reading across the diode and the corresponding milliammeter reading to find the current I flowing through the diode. 6. Gradually, increase the applied voltage (in steps) in the circuit and note the corresponding voltmeter and milliammeter readings in Table E 16.1. The value of current flowing through the diode would be negligibly small till the voltage across the diode exceeds the value of its cut in or threshold voltage. After the cut- in voltage, the variation in current will be rapid. 7. Once the threshold voltage is reached, vary the diode voltage very slowly (preferably in steps of 0.1V) noting the corresponding current I flowing through the diode. Continue increasing voltage till the current reaches the limit of the milliammeter. 8. Now disconnect the circuit and make the connections as shown in Fig. E 16.2 for the reverse bias characteristics. Connect p-side Fig. E 16.2 Reverse biasing for a p-n junction of p-n junction diode to the diode 121 24/04/2018 LABORATORY MANUAL negative terminal of the power supply and replace milliameter with a microammeter. Gradually, increase the applied voltage (in steps) in the circuit and note the corresponding voltmeter and microammeter readings in Table E 16.2. In this part of experiment, with the given supply voltage you will get only flat portion of the reverse bias characteristic curve. CAUTION Never increase the value of the voltage too much across the diode. Excessive current flow may damage the diode if it exceeds its limit. Maximum permissible current that can pass through the diode can be known from the technical data as specified by the manufacturer. O BSERVATIONS 1. p-n junction diode used (diode no.) =... 2. For forward biasing (i) Range of the voltmeter =... V to... V (ii) Least count of the voltmeter scale =... V (iii) Range of the milliammeter =... mA to... mA (iv) Least count of the milliammeter scale =... mA 3. For reverse biasing (i) Range of the voltmeter =... V to... V (ii) Least count of the voltmeter scale =... V (iii) Range of the microammeter =... µA to... µA (iv) Least count the microammeter =... µA Table E 16.1: Variation of forward current with voltage across the diode (forward bias) Sl.No. Forward Forward voltage Vf (V) current If (mA) 1 2 3 - 20 122 24/04/2018  EXPERIMENT 16 13 Table E 16.2: Variation of reverse current with voltage across the diode (reverse bias) Sl.No. Reverse Reverse current voltage Vr (V) Ir (µA) 1 2 -- 20 P LOTTING GRAPH 1. P l o t a g r a p h b e t w e e n forward voltage across the d i o d e ( Vf) a l o n g t h e positive x-axis and current flowing through the diode ( I) a l o n g t h e p o s i t i v e y-axis. The graph as shown in Fig. E 16.3 represents a typical I-V characteristic of a silicon diode used. Locate the knee and determine the cut-in voltage. 2. Now plot the reverse voltage (V r ) along the negative x-axis and the corresponding current (in µA) along the negative y-axis as shown in Fig. E 16.3 Typical I-V characteristics of a silicon diode in forward biasing and reverse Fig. E 16.3. Determine the biasing reverse saturation current. R ESULT A. The value of cut-in voltage for the given diode is... V. B. The reverse saturation current for the given diode is...µA. P RECAUTIONS 1. Find out manufacturer’s specification for maximum permissible 123 LABORATORY MANUAL current through the given diode in forward bias. Take care not to exceed this limit. 2. Find out manufacturers specification for maximum reverse voltage to be applied to the diode. Take care not to exceed this limit. 3. It is important to take care that the potential difference across the diode is increased gradually, in small steps. Keep your eyes on the ammeter and let the current not exceed the specified limit. D ISCUSSION If we use different diodes (Ge or Si), what change do you observe in the I - V characteristics? Does the threshold voltage / cut- in voltage of the diode depend on the material of the diode? S ELF ASSESSMENT 1. How can you operate diode as a switch or as a rectifier? 2. What is the difference between a diode and a resistor? 3. If a resistor of higher value (greater than the resistor connected in the circuit) is connected in series with diode, then comment on the slope of linear region of I - V characteristics. SUGGESTED ADDITIONAL EXPERIMENTS/ACTIVITIES 1. Perform the same experiment with a different value of R connected in series with the diode. What changes will be observed in (a) cut - in voltage? (b) actual value of current for same voltage for different values of R? (c) shape of I - V characteristics? 2. Perform the same experiment with a light emitting diode (LED) in place of a diode and plot the I - V characteristics. What change do you observe in the threshold voltage when you use different coloured LEDs? 124 24/04/2018  E XPERIMENT 13 EXPERIMENT 17 AIM To draw the characteristic curve of a Zener diode and to determine its reverse breakdown voltage. APPARATUS AND MATERIAL REQUIRED A p-n junction Zener diode (IN 758), a variable dc power supply (0-15 V) with least count 0.1 V, a microammeter (0-100 µA), a voltmeter (0-15 V), a resistance of 125 Ω, a high resistance rheostat and connecting wires. PRINCIPLE Zener diodes are essentially p-n junction diodes (both p and n regions are more heavily doped as compared to rectifying p-n junction diode) operated in the breakdown region of the reverse voltage characteristic. These diodes are designated with sufficient power dissipation capacities to work in the breakdown region. The following two mechanisms can cause breakdown in a junction diode: (i) Avalanche breakdown With increasing reverse bias voltage, the electric field across the junction of p-n diode increases. At a certain reverse bias, the electric field imparts a sufficiently high energy to a thermally generated carrier crossing the junction. This carrier, on colliding with a crystal ion on its way, disrupts a covalent bond and produces an electron-hole pair. These carriers on gaining sufficient energy from the applied field collide with other crystal ions and generate further electron-hole pairs. This process is cumulative and produces an avalanche of carriers in a very short time. This mechanism is known as avalanche multiplication, causes large reverse current and the diode is said to work in the region of avalanche breakdown. (ii) Zener breakdown In a Zener diode, both the p and n-sides are heavily doped. Due to the high dopant densities, the depletion layer junction width is small. Since the junction width is small i.e. less than 10–7 m, even a small 125 24/04/2018 LABORATORY MANUAL voltage across it may create a very high field. This high junction field may strip an electron from the valence band which can tunnel to the n-side through the thin depletion layer. Such a mechanism of emission of electrons after applying certain electric field (~ 106 V/m ) or voltage VZ is termed as internal field emission which gives rise to a high reverse current or breakdown voltage. This breakdown is termed as Zener breakdown and the voltage at which it occurs is called Zener voltage. The reverse current at Zener voltage is called Zener current. The very nature of breakdown suggests that the ideal V versus I characteristics (schematically as shown in Fig. E 17.1) of a Zener diode after breakdown will be running parallel to the current axis implying thereby, that a small change in voltage leads to almost infinite or very large change in current. You will appreciate that this is what Fig. E 17.1 Zener diode characteristics curve we have called “breakdown” earlier. However, there is a danger of such a large current flow through the diode that it can result in its excessive heating. To protect the diode from such a damage, normally in practical circuits, we connect a resistance termed as protective resistance (RP ) with the Zener diode which limits the maximum current which can ever pass through the diode. A simple method of determining the approximate value of protective resistance in practical circuits is discussed below: Suppose we are given a Zener diode IN 758 with VZ =10 V. This diode can withstand a maximum power dissipation of 0.4 W (as per the ratings given by the manufacturer). We can find a simple relation between protective Fig. E 17.2 Circuit for Zener diode resistance RP and Zener breakdown voltage. characteristic curve A Zener diode having zener voltage VZ and power dissipation rating PZ is connected across a potential divider arrangement with maximum potential VZ across it (Fig. E 17.2). If the potential drop across the Zener diode is VZ and the rest drops across the protective resistance then we get V = VZ + IZ RP 126 24/04/2018  E XPERIMENT 17 13 PZ Since IZ = (E 17.1) VZ ⎛P ⎞ V = VZ + ⎜ Z ⎟ R P ⎝ VZ ⎠ (V–V Z )V Z (E 17.2) and RP = PZ Therefore a resistance of value R P = (15 − 10 )10 = 125 Ω should be 0.4 connected in series with the Zener diode IN 758 to protect it from damage. P ROCEDURE 1. Note the least count of the given voltmeter and microammeter. 2. The voltmeter and microammeter should read zero with zero applied voltage. If not, then correct the initial reading of the meter suitably. 3. Clean the ends of the connecting wires with the help of sand paper and connect various components by the connecting wires as per the circuit arrangement (Fig. E 17.2). Take care that Zener diode is in reverse bias mode and the ter minal of the microammeter and voltmeter marked positive are connected to the higher potential side of the power supply. 4. Ensure that the microammeter is connected in series with the Zener diode having a series protective resistance R P and voltmeter in parallel to the Zener diode. 5. Switch on the power supply. 6. Move the contact point of the potential divider to apply some reverse bias voltage (V r ). For low reverse bias, the current is negligibly small i.e., of the order of 10 –8 A to 10 –10 A and hence with milliammeter or microammeter, you will observe zero reading. 7. Slowly increase the voltage across the Zener diode in steps and record the value of reverse bias voltage Vr and also record the corresponding reverse current I r from the reading of the microammeter. Take care that the reverse voltage Vr is increased in steps of 0.1 V. 127 24/04/2018 LABORATORY MANUAL O BSERVATIONS 1. Range of the voltmeter =... V to...V 2. Least count of the voltmeter =...V 3. Range of the microammeter =...µA to...µA 4. Least count of the microammeter =...µA 5. Specification of Zener diode used (code no.) =... 6. To calculate the value of protective resistance R P, following data is required. Maximum permissible power (power rating) of the Zener diode specified by the manufacturer, Pz=...W Maximum permissible voltage (voltage rating) of the Zener diode as specified by the manufacturer, Vz=...V Value of the protective resistor to be used in series with the Zener diode, R P =...V (from E 17.2) 7. Note down the reading of the voltmeter and microammeter in Table E 17.1. Table E 17.1: Variation of reverse current Ir with reverse voltage, V r across the Zener diode Sl.No. For Zener diode Voltmeter reading Microammeter Vr (V) Ir (µA) 1 2 -- 10 P LOTTING GRAPH (i) Plot a graph between reverse voltage, Vr and reverse current, Ir taking Vr along x-axis and Ir along y-axis by using the readings from Table E 17.1. (ii) Discuss the nature of Vr – Ir graph and interpret it. (iii) Note the value of the breakdown voltage from the Vr – Ir graph. 128 24/04/2018  E XPERIMENT 17 13 R ESULT The breakdown voltage of the Zener diode obtained from the graph is VZ =... V. P RECAUTIONS 1. Ends of the connecting wires should be cleaned properly with sand paper. 2. Zero reading of voltmeter and microammeter should be checked properly. D ISCUSSION 1. Ideally after breakdown, the current Ir should become infinitely large. Is it so in your case? In case it is not and you find that the current does increase rapidly but not infinitely, then think of the reason. Does the protective resistance or any other contact resistance in the circuit has any role to play in this case? 2. From the manual of electric components, note down the breakdown voltages of the Zener diodes which can be used in any circuit for different voltages. 3. Discuss the role of Zener diode in voltage regulation. S ELF ASSESSMENT 1. What is the principle of Zener diode? 2. How is reverse current obtained? 3. What happens at Zener breakdown? 4. What is meant by internal field emission? 5. How can you use a Zener diode as a voltage regulator? SUGGESTED ADDITIONAL EXPERIMENTS/ACTIVITIES Repeat the experiment using Zener diodes of different code numbers. Do you observe any variation in their reverse breakdown voltages? 129 24/04/2018 LABORATORY MANUAL EXPERIMENT 18 AIM To study the characteristics of a common emitter n-p-n (or p-n-p) transistor and to find out the values of current and voltage gains. APPARATUS AND MATERIAL REQUIRED A transistor (BC 147 or BC 177 or AC 128), a microammeter (0-100 µA), a milliammeter (0-20 mA), two high resistance rheostats, a 100kΩ carbon resistance, two dc power supplies to provide voltage both for input (0-3V) and output (0-15V), two one way keys and connecting wires. PRINCIPLE An n-p-n transistor is made up of a semiconductor such as Ge or Si in which there is a thin p-type layer between two n-type layers. A p-n-p transistor has a thin n-type layer between two p-type layers. The schematic diagram of n-p-n and p-n-p transistors along with their circuit symbols are shown in Fig. E 18.1(a) and E 18.1(b) respectively. Fig. E 18.1 (a) Schematic representations of n-p-n and p-n-p transistors along with their (b) circuit symbols The middle portion of the transistor is called base. It is very thin and lightly doped. Emitter is of moderate size and heavily doped. The collector is moderately doped and larger in size as compared with 130 24/04/2018  E XPERIMENT 18 13 emitter. When a transistor is to be connected in a circuit, one of the terminals has to be common between the input and output. Thus, three circuit configurations are possible. (i) common emitter (CE) configuration (ii) common base (CB) configuration (iii) common collector (CC) configuration. CE configuration When a transistor is used in CE configuration, the input is fed between the base- emitter terminals and the output is derived between the collector - emitter terminals as shown in Fig. E 18.2 (a) and (b). The characteristics o f a t r a n s i s t o r Fig. E 18.2 Input is fed between the base and emitter terminals when the emitter is and the output part is obtained between the collector and emitter terminals in CE configuration in (a) n-p-n kept as a common transistor (b) p-n-p transistor terminal and grounded, the base as input terminal and the collector as output terminals, are called common emitter characteristics. Fig.E 18.3 (a) and (b) show the 131 24/04/2018 LABORATORY MANUAL Fig. E 18.3 Circuit diagram for studying the characteristics of (a) n-p-n transistor (b) p-n-p transistor, in CE configuration circuit diagram for studying the common emitter characteristics of n-p-n and p-n-p transistors respectively. The CE characteristics are of three types: (I) Input characteristics The variation of the input current I B with input voltage V BE keeping output voltage VCE constant is known as input characteristics. As long as the input voltage V BE is less than the knee voltage, current is small and beyond that the current I B rises [Fig. E 18.4(a)]. Thus, the input resistance r i is defined as the ratio of change in base - emitter voltage (∆VBE) to the resulting change in base current (∆I B) at constant collector-emitter voltage (V CE). Also, it is defined as the reciprocal of slope at a fixed point on the input characteristics curve i.e., ⎛ ∆VBE ⎞ ri = ⎜ (E 18.1) ⎝ ∆I B ⎟⎠ V = const. CE The value of r i is of the order of a few hundred Fig. E 18.4 (a) Typical input characteristics of a transistor in CE configuration ohms. (II) Output characteristics The variation in output collector current IC with output voltage VCE for different values of input current I B is known as the output 132 24/04/2018  E XPERIMENT 18 13 characteristics (Fig. E 18.4 (b)). Greater is the value of input current IB greater is the output current IC for a given output voltage VCE. The output resistance r 0 is defined as the ratio of change in collector- emitter voltage (∆VCE) to the change in collector current (∆IC) at constant base current IB. Further it is also defined as the reciprocal of slope at a fixed point on the output characteristics curve i.e., ⎛ ∆VCE⎞ (E 18.2) ro = ⎜ ⎟ ⎝ ∆I C ⎠ I B = const. Fig. E 18.4 (b) Typical output characteristics of a The values of r o are of the order of transistor in CE configuration 50 to 100 kΩ. (III) Transfer characteristics The variation in output collector current IC with input base current I B at constant output voltage V CE is known as the transfer characteristics [Fig. E 18.4(c)]. The current gain β is defined as (E 18.3) Fig. E 18.4 (c) Typical transfer characteristics of a transistor in CE configuration 133 24/04/2018 LABORATORY MANUAL the ratio of the change in collector current (∆I C ) to the change in base current (∆I B ) when the collector to emitter voltage V CE is fixed i.e.,  ∆I C  (E 18.3) β =    ∆I B VCE =const. It is also called forward current gain. Voltage Gain: If ∆Vo is change in the output voltage at the collector for a small voltage change ∆Vi in the emitter base, voltage gain (E 18.4) ∆Vo ∆I C ro ro AV = = ; AV =β ∆Vi ∆I B ri ri P ROCEDURE 1. First check whether the given transistor is n-p-n or p-n-p. 2. Connect the circuit as shown in Fig. E 18.3. (Note that the base- emitter junction is forward biased and the collector-base junction is reverse biased. For example, in an n-p-n transistor; base is given a + ve voltage w.r.t. emitter. Also collector is given a high + ve voltage w.r.t. emitter.) 3. To obtain the input characteristics of the transistor, keep the value of the collector-emitter voltage VCE fixed. First adjust VCE = 0 V and then vary the base-emitter voltage VBE in steps of 0.1 V and for each value of VBE note the base current IB. 4. Repeat step 3 by keeping V CE fixed at three different values. You will observe that I B will continue to be zero for a number of observations i.e., till V BE = 0.6 to 0.7 V for silicon transistor and 0.2 to 0.3 V for germanium transistor. Thereafter, it will increase slowly and then rapidly, till I B is nearly 90per cent of maximum range of the microammeter. 5. To obtain the output characteristics of transistor, keep the base current IB at 10 µA (say). Note the value of collector current IC keeping VCE = 0 V. Now increase the value of VCE very carefully in small steps. Note the corresponding values of IC. (At first the value of IC will increase very rapidly and then increase slowly to almost a constant value [Fig. E 18.4 (b)]. IB should be retained constant as noted earlier. 134 24/04/2018  E XPERIMENT 18 13 6. Repeat step 5 for three different values of IB i.e., say 20 µA, 30 µA, 40 µA. You will observe that when IB increases IC also increases. O BSERVATIONS 1. Range of the voltmeter used in the input circuit =... V to...V 2. Least count of the voltmeter used in the input circuit =... V 3. Range of the voltmeter used in the output circuit =...V to...V 4. Least count of the voltmeter used in the output circuit =... V 5. Range of the microammeter used in the input circuit =... µA to... µA 6. Least count of the microammeter used in the input circuit =... µA 7. Range of the milliammeter used in the output circuit =... mA to...mA 8. Least count of the milliammeter used in the output circuit =... mA 9. Specification of the transistor used =... Table E 18.1: Variation in input current IB with input voltage V BE for fixed value of V C E Sl. No. Input voltage Input current, I B (µA) at VBE =... V VCE =... V VCE =...V VCE =...V VCE =...V 1 2 -- 5 Table E 18.2: Variation in output current IC with output voltage V C E for fixed value of IB Output Output current IC (mA) at Sl. No. voltage VCE VCE =... V I B =... µA I B =...µA I B =...µA IB =...µA 1 2 -- 5 135 24/04/2018 LABORATORY MANUAL For transfer characteristics, using Table E 18.2 note the values of IC corresponding to different values of IB for a fixed value of VCE. Table E 18.3: Variation in output current IC with input current IB for fixed value of V C E Sl. No. Input current Output current, IC (mA) at I B =... µA VCE=... V VCE=... V VCE=... V VCE=... V 1 2 -- 5 P LOTTING GRAPH (i) For input characteristics, plot the graph between input voltage VBE and input current IB for fixed value of VCE, taking VBE along x-axis and IB along y-axis, using the readings from Table E 18.1. (ii) Discuss the nature of VBE versus IB graph and interpret it. (iii) For output characteristics, plot the graph between output voltage VCE and output current IC for fixed value of IB, taking VCE along x-axis and IC along y-axis, using the readings from Table E 18.2. (iv) Discuss the nature of VCE versus IC graph and interpret it. (v) For transfer characteristics, plot the graph between input current IB and output current IC for fixed value of VCE, taking IB along x-axis and IC along y-axis, using the readings from Table E 18.3. (vi) Discuss the nature of IB versus IC graph and interpret it. C ALCULATIONS (i) Draw a tangent on the input characteristics curve at a point on the rapid rising portion [Fig. E 18.4(a)], and from it, determine the reciprocal of slope of the curve at that point. This gives the dynamic input resistance, of the transistor ⎛ ∆V ⎞ ri = ⎜ BE ⎟ ⎝ ∆I B ⎠ V = const. CE (ii) Draw tangents on the output characteristics curve (at linearly rising part A, at turning point B and nearly horizontal part C) 136 24/04/2018  E XPERIMENT 18 13 [Fig. E 18.4(b)]. Measure the reciprocal of slopes which will give the dynamic output resistances, ⎛ ∆V ⎞ r0 = ⎜ CE ⎟ ⎝ ∆I C ⎠ I B = const. at operating points A, B and C [Fig. E18.4(b)]. Note that the dynamic output resistance depends on the operating point. (iii) Find the slope on the transfer characteristics of the transistor to obtain current gain β of the transistor as β=⎜ ⎛ ∆I C ⎞ ⎝ ∆I B ⎟⎠ V CE = const. (iv) Take the values of input resistance r i, output resistance r 0 and current gain β and calculate the value of voltage gain AV of the transistor by using the relation r AV = β ⎛⎜ 0 ⎞⎟ ⎝ ri ⎠ R ESULT For the given transistor (...) in the common emitter (CE) configuration 1. The characteristcs of the transistor are shown in the graphs drawn. 2. At VCE =...V input resistance =...Ω 3. At VBE =...V output resistance =...Ω 4. Current gain, β =... 5. Voltage gain, AV =... P RECAUTIONS (i) Biasing of the transistor should be done considering whether the transistor is n-p-n or p-n-p. (ii) Key should be plugged out to break the circuit when circuit is not in use. 137 24/04/2018 LABORATORY MANUAL D ISCUSSION 1. Is there any change in characteristic curves if we use a p-n-p transistor instead of n-p-n transistor? 2. Why is the input circuit forward biased and output circuit reverse biased? 3. You notice the dynamic output resistance r o is different for different regions of the output characteristic curve. What do you infer from this? 4. If you use some input resistance say 200 Ω at the input then the characteristic curves are called dynamic input characteristics of a CE transistor. The resistors used in the circuit are basically to control the current so as to avoid the burning out or any damage to the transistor. If no resistor is used in the circuit and the experiment is performed, then the characteristics curves are known as the static input characteristics and static output characteristics. While obtaining the static characteristics, extra care has to be taken to avoid any damage to the transistor due to large flow of current beyond the permissible limits. S ELF ASSESSMENT 1. What do you mean by dynamic input resistance and why is it called dynamic? 2. For CE configuration, I C is not cut-off even for I B = 0. For determination of the cut-off voltage in CE mode, how will you reduce IC to zero? 3. Is IC almost independent of VCE for VCE > VBE in CE configuration? SUGGESTED ADDITIONAL EXPERIMENTS/ACTIVITIES Connect the n-p-n transistor in common base configuration. Draw the characteristic curves. Compare input and output characteristic curves of CB and CE configurations. Also find ri and ro. 138 24/04/2018