Electric Circuits Chapter 4-6 PDF

Learning Outcomes Identify the three methods of connecting electrical loads: o Series o Parallel o Series-parallel State the characteristics of a series circuit: o One path for current flow o Supply voltage is equal to the sum of all individual voltages o Total...

Learning Outcomes Identify the three methods of connecting electrical loads: o Series o Parallel o Series-parallel State the characteristics of a series circuit: o One path for current flow o Supply voltage is equal to the sum of all individual voltages o Total resistance is higher than the highest individual resistance State the characteristics of a parallel circuit: o Supply voltage is the same as all branch voltages o Supply or total current is equal to the sum of all individual branch currents o Total resistance is lower than the lowest individual resistance Determine the total resistance of a series circuit comprising two resistors using the formula: RT = R1 + R2 Determine the total resistance of a parallel circuit comprising two resistors using the 1 1 1 formula: = + RT R1 R2 Connect a series circuit comprising two resistors, a voltmeter and an ammeter for the purpose of verifying the characteristics of a series circuit Connect a parallel circuit comprising two resistors, a voltmeter and an ammeter for the purpose of verifying the characteristics of a parallel circuit Recognise that a series-parallel circuit has the characteristics of both series and parallel circuits 1.4.1 Types of Circuit There are basically three types of circuit, which are classified in terms of how their components (or loads) are connected to each other. They are: series circuit; parallel circuit; and series-parallel circuit. Unit 1.4 | Electric Circuit Connections 13  1.4.2 Characteristics of a Series Circuit Fig. 1.4-1: Series circuit (A) There is only one path for the current to flow, that is: IS or IT = I1 = I2 [Is or IT is the total current drawn from the power supply.] (B) The supply voltage, VS or VT, is the sum of all the individual voltages: VS or VT = V1 + V2 (C) The total resistance, RT, is the sum of all the individual resistances: RT = R1 + R2 NOTE: The total resistance is higher than the highest individual resistance in the circuit. 1.4.3 Applying Ohm's Law to a Series Circuit VT = IT × RT V1 = I1 × R1 V2 = I2 × R2 Unit 1.4 | Electric Circuit Connections 14  1.4.4 Worked Examples Fig. 1.4-2: Series circuit Refer to Fig. 1.4-2. (a) Let R1 = 10 Ω, R2 = 20 Ω and VS = 120 V. Determine: (i) the total resistance, RT. RT = R1 + R2 = 10 Ω + 20 Ω = 30 Ω (ii) the supply current, IS. VS IS = RT 120 V = 30 Ω =4A (iii) the voltage across R1, V1. I1 = IS = 4 A V1 = I1 × R1 = 4 A × 10 Ω = 40 V Unit 1.4 | Electric Circuit Connections 15 (b) Let R1 = 40 Ω, IS = 0.5 A and VS = 60 V. Determine: (i) the total resistance, RT. VS RT = IS 60 V = 0.5 A = 120 Ω (ii) the resistance, R2. R2 = RT – R1 = 120 Ω – 40 Ω = 80 Ω (iii) the voltage across R2, V2. I2 = IS = 0.5 A V2 = I2 × R2 = 0.5 A × 80 Ω = 40 V Unit 1.4 | Electric Circuit Connections 16  1.4.5 Practice Questions 802 1917 W 0 2A. I R Ohm's Law Fig. 1.4-3: Series circuit (a) Referring to Fig. 1.4-3, let R1 = 80 Ω, R2 = 160 Ω and IS = 0.2 A. Determine: (i) the total resistance, RT. [240 Ω] RT = R. + R2 = 80m + 402 160 = (ii) the supply voltage, VS. [48 V] R+ 240 = 11s Vs Is Ri = 021s =. o = 0 2Ax. 240r (iii) the voltage across R1, V1. [16 V] = V ],xR , = = 0 2A. +80n = 16V. (iv) the voltage across R2, V2. [32 V] Ve 12 R2 = * = 0 2A x 160m. = 321 Unit 1.4 | Electric Circuit Connections 17  Pg 18.. (b) Two resistors of resistance 50 Ω and 70 Ω respectively, are connected in series with a 100 V supply. Determine: (i) the total resistance of the circuit, RT. [120 Ω] sol 702 RT = RI +R2 1201 I ] = VS IOOV. (ii) the supply current, IS. [0.83 A] V 100V W I= = 1202 = 0833A I R (c) Two resistors (R1 and R2) of resistance 100 Ω and R Ω respectively, are connected in series with a 110 V supply. If the current drawn is 0.5 A, determine the value of R. [120 Ω] 100 R& Ri R2 += 1 Is = 0. 5A NOV I - lov 0. St = 2201 R2 Ri R - - = - = 220n - 100- = 201 Unit 1.4 | Electric Circuit Connections 18  1.4.6 Characteristics of a Parallel Circuit ⑭19 Fig. 1.4-4: Parallel circuit (A) The supply voltage, VS or VT, is equal to all branch voltages, that is: VS or VT = V1 = V2 (B) The supply current (Is) or total current (IT) is equal to the sum of all individual branch currents: IS or IT = I1 + I2 (C) (i) The total resistance is equal to the reciprocal of the sum of the reciprocals of individual resistances: Eg R 102 Ra 201 Parallel.. , = =. Find RT e. 1 1 1 - = + RT R1 R2 = (ii) When there are only two resistors in parallel, the following formula can be used: Please R1 × R2 memorise this RT = R1 + R2 formula. NOTE: The total resistance is lower than the lowest individual resistance in the circuit. 3/12n 5e parallel 102 Re < 5 R +