NEET Physics Chapter 19 Notes PDF

60 Current Electricity 1 E3 Chapter 19 ID Current Electricity (5) For a given conductor current does not change with Electric Current (1) The time rate of flow of charge through any crossΔt 0 i2 i1 Q. Current is a scalar quantity. It's S.I. unit is ampere t D YG then i  ΔQ dQ. If flow is uniform ...

60 Current Electricity 1 E3 Chapter 19 ID Current Electricity (5) For a given conductor current does not change with Electric Current (1) The time rate of flow of charge through any crossΔt 0 i2 i1 Q. Current is a scalar quantity. It's S.I. unit is ampere t D YG then i  ΔQ dQ. If flow is uniform  Δt dt U section is called current. i  Lim change in cross-sectional area. In the following figure i1 = i2 = i3 i3 Fig. 19.2 (A) and C.G.S. unit is emu and is called biot (Bi), or ab ampere. 1A = (1/10) Bi (ab amp.) (2) Ampere of current means the flow of 6.25  1018 (6) Current due to translatory motion of charge : If n particle nq through a given area in time t then i  + t (3) The conventional direction of current is taken to be the U direction of flow of positive charge, i.e. field and is opposite to i ST  E Fig. 19.1 i + + electrons/sec through any cross-section of the conductor. the direction of flow of negative charge as shown below. + + each having a charge q, pass + Fig. 19.3 If n particles each having a charge q pass per second per unit area, the current associated with cross-sectional area A is i  nqA  E If there are n particle per unit volume each having a charge q and moving with velocity v, the current thorough, cross section (4) The net charge in a current carrying conductor is zero. A is i  nqvA Table : 19.1 Types of current Alternating current (ac) (i) Direct current (dc) (i) (Pulsating dc) i (Constant dc) i i + – t t t 2 Current Electricity Magnitude and direction both varies with time dc Inverter ac ac Rectifier dc (ii) Shows heating effect, chemical effect and magnetic effect of 60 (ii) Shows heating effect only current (7) Current due to rotatory motion of charge : If a point charge q is moving in a circle of radius r with speed v (frequency , angular speed  and time period T) then corresponding r Fig. 19.4 q – (1) Current density at point P is given by J  i P n  i J Fig. 19.5 di n dA ˆ dA dA ID q qv qω current i  q ν    T 2 πr 2 π + (iii) It’s symbol is ~ E3 (iii) It’s symbol is  J dA cos U (2) If the cross-sectional area is not normal to the current, (8) Current carriers : The charged particles whose flow in a D YG definite direction constitutes the electric current are called but makes an angle  with the direction of current then J current carriers. In different situation current carriers are different. (i) Solids : In solid conductors like metals current carriers are free electrons. (ii) Liquids : In liquids current carriers are positive and U negative ions. (iii) Gases : In gases current carriers are positive ions and ST free electrons. (iv) Semi conductor : In semi conductors current carriers are holes and free electrons. Current Density (J ) di  di  JdA cos  J.dA  i   J  dA dA cos (3) If current density J is uniform for a normal crosssection A then J  i A (4) Current density J is a vector quantity. It's direction is same as that of E. It's S.I. unit is amp/m2 and dimension [L–2A]. (5) In case of uniform flow of charge through a crosssection normal to it as i  nqvA  J  (6) J  E  Current E  i  nqv. A density relates with electric field as ; where  = conductivity and  = resistivity or specific resistance of substance. Drift Velocity Current density at any point inside a conductor is defined Drift velocity is the average uniform velocity acquired by as a vector having magnitude equal to current per unit area free electrons inside a metal by the application of an electric surrounding that point. Remember area is normal to the field which is responsible for current through it. Drift velocity is direction of charge flow (or current passes) through that point. very small it is of the order of 10–4 m/s as compared to thermal l speed (~– 10 5 m / s) of electrons at room temperature. A vd E + V – Fig. 19.6 Current Electricity 1039 metallic  lattice is defined as relaxation time mean free path . With rise in temperature  r.m.s. velocityof electrons v rms vrms increases consequently  decreases. (2) Mobility : Drift velocity per unit electric field is called mobility of electron i.e.   If suppose for a conductor n = Number of electron per unit volume of the conductor 60 Ohm's Law vd m2. It’s unit is. volt  sec E If the physical conditions of the conductor (length, temperature, mechanical strain etc.) remains some, then the V = potential difference across the conductor current flowing through the conductor is directly proportional to E = electric field inside the conductor the potential difference across it’s two ends i.e. i  V i = current, J = current density,  = specific resistance,  =  1 conductivity     then current relates with drift velocity as   d we can also write vd  V  iR where R is a proportionality constant, known as electric resistance. (1) Ohm’s law is not a universal law, the substances, which E i J E V    . ne  l n e neA ne ne obey ohm’s law are known as ohmic substance. (2) Graph between V and i for a metallic conductor is a U (1) The direction of drift velocity for electron in a metal is  opposite to that of applied electric field (i.e. current density J ). v d  E i.e., greater the electric field, larger will be the drift D YG velocity. straight line as shown. At different temperatures V-i curves are different. V V T1 1 (2) When a steady current flows through a conductor of non-uniform cross-section drift velocity varies inversely with 1  area of cross-section  v d   A  vd1 vd 2 i A1 < A2 so vd1  vd 2 i  ID i  neAv E3 A = Area of cross-section A1 T2 2  1 2 i i (A) Slope of the line = tan   V (B) Here tan1 > tan2 So R1 > R2  R i A2 i.e. T1 > T2 Fig. 19.9 ST U Fig. 19.7 (3) If diameter (d) of a conductor is doubled, then drift velocity of electrons inside it will not change. + + V – V – Less – d More – d Same – vd Some – vd Fig. 19.8 (3) The device or substances which don’t obey ohm’s law e.g. gases, crystal rectifiers, thermoionic valve, transistors etc. are known as non-ohmic or non-linear conductors. For these V-i Crystal i Static resistance R st  (1) Relaxation time () : The time interval between two successive collisions of electrons with the positive ions in the rectifier curve is not linear. V 1  i tan    V Fig. 19.10 1040 Current Electricity Dynamic resistance R dyn  V 1  I tan  gives R2 = R1 [1 +  (t2 – t1)]. This formula gives an approximate value. Resistance Table 19.2 : Variation of resistance of some electrical material (1) The property of substance by virtue of which it with temperature opposes the flow of current through it, is known as the Material Temp. coefficient of Variation of resistance resistance () with temperature rise Metals Positive Increases Solid non-metal Zero Independent Semi-conductor Negative of a conductor A = Area of cross-section of conductor, n = No. of free electrons per unit volume in conductor,  = relaxation R time then resistance of conductor l l m . ; where  = resistivity of the material of 2 A ne  A conductor (3) Unit and dimension : It’s S.I. unit is Volt/Amp. or Ohm (). Electrolyte Negative Decreases Ionised gases Negative Decreases Alloys Small positive value Almost constant 8 1volt 10 emu of potential  = 109 emu of 1 Amp 10 1 emu of current ID Also 1 ohm  resistance. It’s dimension is [ML2 T 3 A 2 ]. (4) Dependence of resistance : Resistance of a conductor depends upon the following factors. Resistivity (), Conductivity () and Conductance (C) U (1) Resistivity : From R   (i) Length of the conductor : Resistance of a conductor is directly proportional to it’s length i.e. R  l and inversely D YG 1 proportional to it’s area of cross-section i.e. R  A (ii) Temperature : For a conductor substance having unit area of cross-section and unit length. (i) Unit and dimension : It’s S.I. unit is ohm  m and dimension is [ML3 T 3 A 2 ] (ii) It’s formula :   R0 = resistance of conductor at 0oC Rt = resistance of conductor at toC U and ,  = temperature co-efficient of resistance then Rt  R0 (1   t   t 2 ) for t > 300oC and ST Rt  R0 (1  t ) for t  300oC or   Rt  R0 R0  t If R1 and R2 are the resistances at t1oC and t2oC R 1   t1 respectively then 1 . R2 1   t2 The value of  is different at different temperature. Temperature coefficient of resistance averaged over the R 2  R1 temperature range t1oC to t2oC is given by   which R1 (t 2  t1 ) l ; If l = 1m, A = 1 m2 then A R   i.e. resistivity is numerically equal to the resistance of a Resistance  temperatur e. If Decreases E3 (2) Formula of resistance : For a conductor if l = length 60 resistance. m ne 2 (iii) Resistivity is the intrinsic property of the substance. It is independent of shape and size of the body (i.e. l and A). (iv) For different substances their resistivity is also different e.g. silver = minimum = 1.6  10–8 -m and fused quartz = maximum  1016 -m insulator (Maximum for fused quartz)   alloy   semi - conductor   conductor (Minimum for silver ) (v) Resistivity depends on the temperature. For metals t  0 (1  t) i.e. resitivity increases with temperature. (vi) Resistivity increases with impurity and mechanical stress. Current Electricity 1041 except iron, cobalt and nickel. (viii) Resistivity of certain substances like selenium, cadmium, sulphides is inversely proportional to intensity of light falling upon them. (2) Conductivity : Reciprocal of resistivity is called conductivity () i.e.   1 of resistances before l R1 l A  1  2  1 R2 l 2 A1  l 2  A   2  A   1 2 and (2) If radius is given then R  2 r    2 r    1 (1) If length is given then R  l 2  with unit mho/m and dimensions  after 4 stretching d    2  d   1 R1  l1  R 2  l 2         4 2 r  R 1  1   2  R 2  r1  r4 4 Electrical Conducting Materials For Specific Use [M 1 L3 T 3 A 2 ]. (1) Filament of electric bulb : Is made up of tungsten which has high resistivity, high melting point. E3 (3) Conductance : Reciprocal of resistance is known as conductance. C  Ratio 60 (vii) Magnetic field increases the resistivity of all metals 1 1 It’s unit is or –1 or “Siemen”. R  (2) Element of heating devices (such as heater, geyser or i press) : Is made up of nichrome which has high resistivity and ID high melting point.  (3) Resistances of resistance boxes (standard resistances) V : Are made up of alloys (manganin, constantan or nichrome) Fig. 19.11 U these materials have moderate resistivity which is practically independent of temperature so that the specified value of D YG Stretching of Wire If a conducting wire stretches, it’s length increases, area of cross-section decreases so resistance increases but volume remain constant. Suppose for a conducting wire before stretching it’s length = l1, area of cross-section = A1, radius = r1, diameter = d1, and l1 A1 U resistance R1   Before stretching ST l1  After stretching (4) Fuse-wire : Is made up of tin-lead alloy (63% tin + 37% lead). It should have low melting point and high resistivity. It is used in series as a safety device in an electric circuit and is designed so as to melt and thereby open the circuit if the current exceeds a predetermined value due to some fault. The function of a fuse is independent of its length. Safe current of fuse wire relates with it’s radius as i  r 3/2. l2  (5) Thermistors : A thermistor is a heat sensitive resistor Volume remains constant i.e. A1l1 = A2l2 Fig. 19.12 usually prepared from oxides of various metals such as nickel, copper, cobalt, iron etc. These compounds are also semiconductor. For thermistors  is very high which may be positive After stretching length = l2, area of cross-section = A2, radius = r2, diameter = d2 and resistance  R2   resistance does not alter with minor changes in temperature. l2 A2 or negative. The resistance of thermistors changes very rapidly with change of temperature. i V Fig. 19.13 1042 Current Electricity and to measure very low temperature. Orange 3 103 Y Yellow 4 104 G Green 5 105 B Blue 6 106 V Violet 7 107 G Grey 8 108 W White 9 109 60 Thermistors are used to detect small temperature change O Colour Coding of Resistance To remember the sequence of colour code following To know the value of resistance colour code is used. These sentence should kept in memory. E3 code are printed in form of set of rings or strips. By reading the B B R O Y Great Britain Very Good Wife. values of colour bands, we can estimate the value of resistance. The carbon resistance has normally four coloured rings or Grouping of Resistance (1) Series grouping bands say A, B, C and D as shown in following figure. C D (i) Same current flows through each resistance but potential ID A B difference distributes in the ratio of resistance i.e. V  R U Fig. 19.14 D YG Colour band A and B : Indicate the first two significant R1 R2 R3 V1 V2 V3 i + V – Fig. 19.15 figures of resistance in ohm. Band C : Indicates the decimal multiplier i.e. the number of Band D : Indicates the tolerance in percent about the than the maximum value of resistance in the combination. (iii) If n identical resistance are connected in series indicated value or in other words it represents the percentage U accuracy of the indicated value. The tolerance in the case of gold is  5% and in silver is  R eq  nR V'  and potential difference across each resistance V n ST 10%. If only three bands are marked on carbon resistance, then Req  R1  R 2  R 3 equivalent resistance is greater (ii) zeros that follows the two significant figures A and B. Figure Multiplier but current distributes in the aid to memory (A, B) (C) reverse ratio of their resistance it indicate a tolerance of 20%. Table 19.3 : Colour code for carbon resistance Letters as an Colour B Black 0 10o B Brown 1 101 R Red 2 102 (2) Parallel grouping i1 i2 (i) Same potential difference appeared across each resistance i.e. i  1 R i3 i R1 R2 R3 V Fig. 19.16 Current Electricity 1043 (ii) Equivalent resistance is given by 1 1 1 1    R eq R1 R 2 R 3 R1 R 2 R 3 R1 R 2  R 2 R 3  R 2 R1 or R eq  (R11  R 21  R 31 )1 or R eq  Equivalent resistance is smaller than the minimum value of resistance in the combination. terminals of a cell when it is not supplying any current is called (iv) If two resistance in parallel R1 R 2 Multiplication   R1  R 2 Addition it’s emf. (2) Potential difference (V) : The voltage across the (v) Current through any resistance terminals of a cell when it is supplying current to external  Resistance of oppositebranch  i'  i    Total resistance   resistance is called potential difference or terminal voltage. E3 Potential difference is equal to the product of current and Where i = required current (branch current), i1 i = main current resistance of that given part i.e. V = iR. R1 (3) Internal resistance (r) : In case of a cell the opposition  R1 and i2  i   R1  R 2     of electrolyte to the flow of current through it is called internal i2 ID     i R2 resistance of the cell. The internal resistance of a cell depends on the distance between electrodes (r  d), area of electrodes [r Fig. 19.17  (1/A)] and nature, concentration (r  C) and temperature of U  R2 i1  i   R1  R 2 (vi) In n identical resistance are connected in parallel i R and current through each resistance i'  n n D YG R eq  60 R eq (1) Emf of cell (E) : The potential difference across the ST U Cell electrolyte [r  (1/ temp.)]. A cell is said to be ideal, if it has zero internal resistance. Cell in Various Positions (1) Closed circuit : Cell supplies a constant current in the R circuit. i V = iR E, r Fig. 19.19 The device which converts chemical energy into electrical energy is known as electric cell. Cell is a source of constant emf but not constant current. Anode Cathode A E Rr + (ii) Potential difference across the resistance V  iR – (iii) Potential drop inside the cell = ir – + (i) Current given by the cell i  + – – + Symbol of cell Electrolyte Fig. 19.18 (iv) Equation of cell E  V  ir (E > V) E  (v) Internal resistance of the cell r    1   R V  (vi) Power dissipated in external resistance (load) 1044 Current Electricity (i) 2 P  Vi  i 2 R  V2  E   .R R R r Power delivered will be maximum when Pmax  Rr so 2 Maximum current (called short circuit current) flows momentarily isc  E r (ii) Potential difference V = 0 E. 4r This statement in generalised from is called “maximum power transfer theorem”. Grouping of Cells 60 Pmax = E2/4r P R Fig. 19.20 E3 R=r Group of cell is called a battery. the cell then E = V – ir and E < V. subtractive while their internal resistances are always additive. If (2) Open circuit : When no current is taken from the cell it dissimilar plates of cells are connected together their emf’s are R A D B D YG C U added to each other while if their similar plates are connected is said to be in open circuit E, r Fig. 19.21 (i) In series grouping of cell’s their emf’s are additive or ID (vii) When the cell is being charged i.e. current is given to Current through the circuit i = 0 U (ii) Potential difference between A and B, VAB = E together their emf’s are subtractive. E1 E2 E1 E2 Eeq = E1 – E2 (E1 > E2) Eeq = E1 + E2 req = r1 + r2 req = r1 + r2 Fig. 19.23 (1) Series grouping : In series grouping anode of one cell is connected to cathode of other cell and so on. If n identical cells E, r are connected in series E, r E, r E, r (iii) Potential difference between C and D, VCD = 0 ST (3) Short circuit : If two terminals of cell are join together by a thick conducting wire R=0 E, r Fig. 19.22 i R Fig. 19.24 (i) Equivalent emf of the combination Eeq  nE (ii) Equivalent internal resistance req  nr (iii) Main current = Current from each cell  i  nE R  nr (iv) Potential difference across external resistance V  iR Current Electricity 1045 (v) Potential difference across each cell V '  V n 2  nE  (vi) Power dissipated in the external circuit   .R  R  nr  (vii) Condition for maximum power R  nr and  E2   Pmax  n    4r  (i) Equivalent emf of the combination Eeq  nE (2) Parallel grouping : In parallel grouping all anodes are (ii) Equivalent internal resistance of the combination req E, r nr  m E3 connected at one point and all cathode are connected together at other point. If n identical cells areEconnected ,r in parallel 60 (viii) This type of combination is used when nr > R (3) Mixed Grouping : If n identical cell’s are connected in a row and such m row’s are connected in parallel as shown. E, r E, r 1 1 E, r n 2 entering the junction must equal the sum of the currents leaving the junction. i1  i3  i2  i4 (ii) This law is simply a statement of “conservation of charge”. 2 i In a circuit, at any junction the sum of the currents m V R Fig. 19.26 1046 Current Electricity (2) Kirchoff’s second law : This law is also known as loop rule or voltage law (KVL) and according to it “the algebraic sum of the changes in potential in complete traversal of a mesh (iv) The change in voltage in traversing an inductor in the direction of current is  L Adi L (closed loop) is zero”, i.e. V = 0 dt. L i B L (A) (i) This law represents “conservation of energy”. L di dt B (B) 60 (3) Sign convention for the application of Kirchoff’s law : For the application of Kirchoff’s laws following sign convention E3 Different Measuring Instruments (i) The change in potential in traversing a resistance in the direction of current is – iR while in the opposite direction +iR B – iR A R i B ID R i di L i Fig. 19.31 independent equations in accordance with loop rule will be (n – 1). A A dt (ii) If there are n meshes in a circuit, the number of are to be considered di while in opposite direction it is dt + iR U Fig. 19.28 (ii) The change in potential in traversing an emf source from negative to positive terminal is +E while in the opposite D YG direction – E irrespective of the direction of current in the circuit. E A B –E E A B +E Fig. 19.29 U (iii) The change in potential in traversing a capacitor from the negative terminal to the positive terminal is  q. C ST opposite direction  A – C B + q (A)  A q C Fig. 19.30 –  q C C q while in C (1) Galvanometer : It is an instrument used to detect small current passing through it by showing deflection. Galvanometers are of different types galvanometer, moving magnet e.g. moving coil galvanometer, hot wire galvanometer. In dc circuit usually moving coil galvanometer are used. (i) It’s symbol : ; where G is the G total internal resistance of the galvanometer. (ii) Full scale deflection current : The current required for full scale deflection in a galvanometer is called full scale + q (B) B deflection current and is represented by ig. (iii) Shunt : The small resistance connected in parallel to galvanometer coil, in order to control current flowing through the galvanometer is known as shunt. Table 19.4 : Merits and demerits of shunt Merits of shunt Demerits of shunt Current Electricity 1047 To protect the galvanometer Shunt resistance coil from burning the sensitivity of galvanometer. (c) To pass nth part of main current (i.e. ig  decreases the galvanometer, required shunt S  It can be used to convert any i ) through n G. (n  1) (3) Voltmeter : It is a device used to measure potential galvanometer into ammeter of difference and is always put in parallel with the ‘circuit element’ (2) Ammeter : It is a device used to measure current and across which potential difference is to be measured. V 60 desired range. is always connected in series with the ‘element’ through which current is to be measured. R i R + i + V – E3 A V Fig. 19.34 – ID Fig. 19.32 (i) The reading of a voltmeter is always lesser than true value. actual current in the circuit. be its reading. A voltmeter is said to be ideal if its resistance is infinite, i.e., it draws no current from the circuit element for its D YG (ii) Smaller the resistance of an ammeter more accurate will be its reading. An ammeter is said to be ideal if its resistance r is zero. (ii) Greater the resistance of voltmeter, more accurate will U (i) The reading of an ammeter is always lesser than (iii) Conversion of galvanometer into ammeter : A galvanometer may be converted into an ammeter by connecting operation. (iii) Conversion of galvanometer into voltmeter : A galvanometer may be converted into a voltmeter by connecting R a large resistance R in series with the galvanometer as shown G in the figure. a low resistance (called shunt S) in parallel to the galvanometer Vg = igG S V U G as shown in figure. i (V – Vg) ig i – ig Fig. 19.35 G ST ig Ammeter Fig. 19.33 (a) Equivalent resistance of the combination = G + R (b) According to ohm’s law (a) Equivalent resistance of the combination  GS GS (b) G and S are parallel to each other hence both will have equal potential difference i.e. ig G  (i  ig )S ; which gives Required shunt S  ig (i  i g ) G V = ig (G + R); which gives Required series resistance R    V V G  1G   ig   Vg (c) If nth part of applied voltage appeared across galvanometer (i.e. Vg  R  (n  1) G. V ) then required series resistance n 1048 Current Electricity (4) Wheatstone bridge Potentiometer is a device mainly used to measure emf of a B arrangement of P four resistance which can be A used to measure one of K1 them in terms of rest. Here G (1) Circuit diagram : Potentiometer consists of a long S – arms AB and BC are called measure internal resistance of a given cell. C R + given cell and to compare emf’s of cells. It is also used to Q D resistive wire AB of length L (about 6m to 10 m long) made up K2 of mangnine or constantan and a battery of known voltage e Fig. 19.36 and internal resistance r called supplier battery or driver cell. ratio arm and arms AC and BD are called conjugate arms 60 : Wheatstone bridge is an Connection of these two forms primary circuit. One terminal of another cell (whose emf E is to be measured) is connected at one end of the main circuit and the when deflection in galvanometer is zero i.e. no current flows other terminal at any point on the resistive wire through a through the galvanometer or in other words VB = VD. In the P R balanced condition , on mutually changing the position  Q S Primary are as follows circuit circuit will flow from D to B if VD > VB i.e. (VA  VD )  (VA  VB ) which J A Secondary (ii) Unbalanced bridge : If the bridge is not balanced current E B G Fig. 19.38 U gives PS > RQ. R h ,r galvanometer G. This eforms theKsecondary circuit. Other details ID of cell and galvanometer this condition will not change. E3 (i) Balanced bridge : The bridge is said to be balanced (iii) Applications of wheatstone bridge : Meter bridge, post D YG office box and Carey Foster bridge are instruments based on the principle of wheatstone bridge and are used to measure unknown resistance. J = Jockey (5) Meter bridge : In case of meter bridge, the resistance K = Key wire AC is 100 cm long. Varying the position of tapping point B, R = Resistance of potentiometer wire, bridge is balanced. If in balanced position of bridge AB = l, BC P R Q (100  l) (100  l) (100 – l) so that. Also  S    R Q SS l P l B ST P l cm Q (i) The specific resistance () of potentiometer wire must be high but its temperature coefficient of resistance () must be K Fig. 19.37 Rh = Variable resistance which controls the current C (100 – l) cm E = Specific resistance of potentiometer wire. through the wire AB G A  R.B. U R low. (ii) All higher potential points (terminals) of primary and secondary circuits must be connected together at point A and all lower potential points must be connected to point B or jockey. Potentiometer Current Electricity 1049 (iii) The value of known potential difference must be greater than the value of unknown potential difference to be measured. (iv) The potential gradient must remain constant. For this the current in the primary circuit must remain constant and the everywhere. (2) Potential gradient (x) : Potential difference (or fall in potential) per unit length of wire is called potential gradient i.e. x If V < E then current will flow in galvanometer circuit in opposite direction If V = E then no current will flow in galvanometer circuit   e V volt .R. where V  iR    R  R  r L m h   So one direction this condition to known as null deflection position, length l is known as balancing length. V iR iρ e R   . L L A (R  R h  r) L ID x If V > E then current will flow in galvanometer circuit in 60 (v) The diameter of potentiometer wire must be uniform E3 jockey must not be slided in contact with the wire. In balanced condition E  xl (i) Potential gradient directly depends upon or E  xl  U (a) The resistance per unit length (R/L) of potentiometer   R V iR e .  l l l    L L  R  Rh  r  L If V is constant then L  l  wire. section) (c) The D YG (b) The radius of potentiometer wire (i.e. Area of cross- specific resistance of the material of x1 L l  1  1 x 2 L2 l2 (6) Standardization of potentiometer : The process of determining potential gradient experimentally is known as standardization of potentiometer. potentiometer wire (i.e. ) e, r Rh K (d) The current flowing through potentiometer wire ( i) (ii) potential gradient indirectly depends upon U (a) The emf of battery in the primary circuit ( i.e. e) (b) The resistance of rheostat in the primary circuit ( i.e. E0 B G E Fig. 19.40 ST Rh) J A (3) Working : Suppose jocky is made to touch a point J on wire then potential difference between A and J will be V  xl At this length (l) two potential difference are obtained Let the balancing length for the standard emf E0 is l0 then (i) V due to battery e and by the principle of potentiometer E0 = xl0  x  (ii) E due to unknown cell e, r l J1 A Rh K G J J2 G G E Fig. 19.39 B E0 l0 1050 Current Electricity (7) Sensitivity of potentiometer : A potentiometer is said to be more sensitive, if it measures a small potential difference more accurately. (i) Initially in secondary circuit key K' remains open and balancing length (l1) is obtained. Since cell E is in open circuit (i) The sensitivity of potentiometer is assessed by its so it’s emf balances on length l1 i.e. E = xl1 potential gradient. The sensitivity is inversely proportional to the potential gradient. …. (i) (ii) Now key K is closed so cell E comes in closed circuit. If the process of balancing repeated again then potential difference V balances on length l2 i.e. V = xl2 (a) The resistance in primary circuit will have to be …. (ii) E  (iii) By using formula internal resistance r    1 . R ' V  decreased. E3 (b) The length of potentiometer wire will have to be increased l l r   1 2  l2 so that the length may be measured more accuracy. Table 19.5 : Difference between voltmeter and potentiometer Potentiometer Its resistance is infinite It draws some current from It does not draw any current from source of emf the source of unknown emf The potential difference The potential difference measured by it is lesser than measured by it is equal to the actual potential difference actual potential difference Its sensitivity is low Its sensitivity is high (2) Comparison of emf’s of two cell : Let l1 and l2 be the balancing lengths with the cells E1 and E2 respectively then E1 = E1 l1  E 2 l2 K e, r xl1 and E2 = xl2  U It’s resistance is high but finite Rh J B A D YG It is a versatile instrument  . R'   ID Voltmeter 60 (ii) In order to increase the sensitivity of potentiometer E1 G 1 E2 2 Fig. 19.42 It measures only emf or potential difference It is based on zero deflection method method U It is based on deflection Let E1 > E2 and both are connected in series. If balancing ST Application of Potentiometer length is l1 when cell assist each other and it is l2 when they (1) To determine the internal resistance of a primary cell Rh K e, r + J A K Fig. 19.41 E1 – + E2 + – E1 – – E2 B G E R oppose each other as shown then : (E1  E 2 )  xl 1  E1  E 2 l  1 E1  E 2 l2 (E1  E 2 )  xl 2 or E1 l l  1 2 E 2 l1  l2 + Current Electricity 1051 (3) Comparison of resistances : Let the balancing length for resistance R1 (when XY is connected) is l1 and let balancing length for resistance R1 + R2 (when YZ is connected) is l2. Y R1 i where L = length of potentiometer wire,  = resistance per unit length, l = balancing ammeter readings with the help of potentiometer is called B calibration of ammeter. Z (i) In the process of calibration of an ammeter the current flowing in a circuit is measured by an ammeter and the same R2 current is also measured with the help of potentiometer. By Rh comparing both the values, the errors in the ammeter readings E3 K1 1 Fig. 19.43 e are determined. A K1 + – + E1 + – R 2 l2  l1   R1 l1 – R Rh K U + A D YG HRB 1 + (4) To determine thermo emf 1 2 ID Then iR1 = xl1 and i(R1 + R2) = xl2 A iRl L 60 X G  e (5) Calibration of ammeter : Checking the correctness of J A iR L length for e Rh K (iv) x  i  – B G 3 + A – K2 Fig. 19.45 B G + E0 – G 1 2 3 Cold ice Hot sand U Fig. 19.44 (ii) For the calibration of an ammeter, 1  standard resistance coil is specifically used in the secondary circuit of the potentiometer, because the potential difference across 1  is equal to the current flowing through it i.e. V = i. (iii) If the balancing length for the emf E0 is l0 then E0 = xl0 (i) The value of thermo-emf in a thermocouple for ordinary ST temperature difference is very low (10–6 volt). For this the x  E0 l0 (Process of standardisation) potential gradient x must be also very low (10–4 V/m). Hence a (iv) Let i ' current flows through 1 resistance giving high resistance (R) is connected in series with the potentiometer potential difference as V '  i' (1)  xl1 where l1 is the balancing wire in order to reduce current. (ii) The potential difference across R must be equal to the emf of standard cell i.e. iR = E0  i  E0 R (iii) The small thermo emf produced in the thermocouple e = xl length. So error can be found as i  i  i'  i  xl1  i  E0  l1 l0 (6) Calibration of voltmeter (i) Practical voltmeters are not ideal, because these do not have infinite resistance. The error of such practical voltmeter 1052 Current Electricity can be found by comparing the voltmeter reading with conductor is zero. calculated value of p.d. by potentiometer. (ii) If l0 is balancing length for E0 the emf of standard cell by connecting 1 and 2 of bi-directional key, then x = E0/l0. (iii) The balancing length l1 for unknown potential difference V is given by (by closing 2 and 3) V '  xl1  (E0 / l0 )l1.  For a given conductor JA = i = constant so that J  Rh K1 60 e + – C E0 1 + – + V 2 – G 3 RB + i.e., J1 A1 = J2 A2 ; this is called equation of continuity B E3 + A K2 – 1 A Rh Fig. 19.46 ID  The drift velocity of electrons is small because of the frequent collisions suffered by electrons.  The small value of drift velocity produces a large amount of electric current, due to the presence of extremely large U If the voltmeter reading is V then the error will be ( V – V) D YG which may be + ve, – ve or zero.  Human body, though has a large resistance of the order of number of free electrons in a conductor. The propagation of current is almost at the speed of light and involves electromagnetic process. It is due to this reason that the electric bulb glows immediately when switch is on.  In the absence of electric field, the paths of electrons between successive collisions are straight line while in presence of electric field the paths are generally curved. k (say 10 k), is very sensitive to minute currents even as U low as a few mA. Electrocution, excites and disorders the  Free electron density in a metal is given by n  N Ax d A where NA = Avogadro number, x = number of free electrons activity of the body. per atom, d = density of metal and A = Atomic weight of  dc flows uniformly throughout the cross-section of metal. conductor while ac mainly flows through the outer surface  In the absence of radiation loss, the time in which a fuse will area of the conductor. This is known as skin effect. melt does not depends on it’s length but varies with radius as  It is worth noting that electric field inside a charged t  r4. conductor is zero, but it is non zero inside a current carrying  If length (l) and mass (m) of a conducting wire is given ST nervous system of the body and hence one fails to control the conductor and is given by E  V l where V = potential difference across the conductor and l = length of the conductor. + + + +Electric + + field out side the l current carrying Ein = 0 + + + + J1 + i + A+1 i J2 Ein = V/l A2 – then R  l2. m  Macroscopic form of Ohm’s law is R  V , while it’s i Current Electricity 1053 microscopic form is J =  E.  After stretching if length increases by n times then resistance will increase by n2 times i.e. R 2  n 2 R1. Similarly 1 if radius be reduced to times then area of cross-section n n2 times so the resistance becomes n times i.e. 4 The diagonal of face (e.g. AC, ED,....)  A side (e.g. AB, BC.....)  R 2  n 4 R1.  After stretching if length of a conductor increases by x% 5 R 6 3 R 4 7 R 12 60 decreases 1 The longest diagonal (EC or AG)   Resistance of a conducting body is not unique but depends on it’s length and area of cross-section i.e. how the  Decoration of lightning in festivals is an example of potential difference is applied. See the following figures series grouping whereas all household appliances connected in parallel grouping. E3 then resistance will increases by 2x % (valid only if x < 10%) c c  ID  Using n conductors of equal resistance, the number of b a possible combinations is 2n – 1.  b a the number of possible combinations will be 2n. U  If the resistance of n conductors are totally different, then  If n identical resistances are first connected in series and by Rp Rs  n2. 1 D YG then in parallel, the ratio of the equivalent resistance is given Length = a Length = b Area of cross-section = b  c Area of cross-section = a  c  a   bc  If a wire of resistance R, cut in n equal parts and then these parts are collected to form a bundle then equivalent resistance of combination will be R n2 U be Rs and Rp R1. respectively Resistance R     Some standard results for equivalent resistance A then R2 B R5  If equivalent resistance of R1 and R2 in series and parallel  b   ac Resistance R    R3 R4 ST 1 1 R1   Rs  Rs2  4 Rs R p  and R2   Rs  Rs2  4 Rs R p .   2  2   If a skeleton cube is made with 12 equal resistance each having resistance R then the net resistance across H E R1 R2 (R3  R4 )  (R1  R2 )R3 R4  R5 (R1  R2 ) (R3  R4 ) R5 (R1  R2  R3  R4 )  (R1  R3 )(R2  R4 ) G F D A R AB  R1 A B R3 C B R2 R2 R1 1054 Current Electricity present in that branch. In practical situation it always happen because we can never have an ideal cell or battery with zero resistance. 2 R1 R2  R3 (R1  R2 ) 2 R3  R1  R2 A R1 R1 R1 connected then it will cancel out the effect of two cells e.g. If R1 in the combination of n identical cells (each having emf E and R3 R3 B  In series grouping of identical cells. If one cell is wrongly R3 R3  internal resistance r) if x cell are wrongly connected then equivalent emf R2 R2 R2 R2 60 R AB  Eeq  (n  2 x ) E resistance req  nr. and equivalent internal   V 1/2 1 1 (R1  R2 )  (R1  R2 )2  4 R3 (R1  R2 ) 2 2 R1 R1 R1 R2 R2 B R1 R2  ID A U R AB  E3  Graphical view of open circuit and closed circuit of a cell. Vmax =E; i = 0 imax =E/r ; V = 0 i  If n identical cells are connected in a loop in order, then R 1  R1 1  1  4  2 2   R1      D YG R AB  emf between any two points is zero. E, r  It is a common misconception that “current in the circuit Close E, r loop will be maximum when power consumed by the load is maximum.” E, r E, r E, r n cell Actually current i  E /(R  r) is maximum (= E/r) when R = U min = 0 with PL  (E / r)2  0  0 min. while power consumed by the load E2R/(R + r)2 is maximum (= E2/4r) when R = r and ST i  (E / 2r)  max(  E / r).  In parallel grouping of two identical cell having no internal resistance R  Emf is independent of the resistance of the circuit and R E depends upon the nature of electrolyte of the cell while E E potential difference depends upon the resistance between the E two points of the circuit and current flowing through the circuit.  Whenever a cell or battery is present in a branch there must be some resistance (internal or external or both) E eq  E  E eq  0 When two cell’s of different emf and no internal resistance are connected in parallel then equivalent emf is R E1 Current Electricity 1055 indeterminate, note that connecting a wire with a cell with no resistance is equivalent to short circuiting. Therefore the total 60 current that will be flowing will be infinity. equivalent emf E1r2  E2r1 r1  r2 i E1,r1 i2 E2, r2 R U Eeq  i1 ID are connected with reversed polarity as shown then  Wheatstone bridge is most sensitive if all the arms of D YG bridge have equal resistances i.e. P = Q = R = S  If the temperature of the conductor placed in the right gap of metre bridge is increased, then the balancing length decreases and the jockey moves towards left.  In Wheatstone bridge to avoid inductive effects the battery key should be pressed first and the galvanometer key afterwards. U  The measurement of resistance by Wheatstone bridge is not affected by the internal resistance of the cell.  In case of zero deflection in the galvanometer current ST E3  In the parallel combination of non-identical cell's if they flows in the primary circuit of the potentiometer, not in the galvanometer circuit.  A potentiometer can act as an ideal voltmeter.