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EXPERIMENT 2 SERIES AND PARALLEL RESISTANCE CIRCUITS Aim: 1. To show that the total resistance of resistors connected in series is the sum of the individual resistances of the resistors. 2. To show that the total conductance of resistors in parallel is equal to the summation of individual conductances of the resistors. I. Introduction (a) In series circuit connection resistors are connected one after the other and hence the same current flows in the circuit. Consider the series circuit composed of two resistors shown in Figure 1 below. R1 Req R2 I I + V - (a) + V - (b) Figure 1 Series Circuit Kirchhoff’s Voltage Law when applied to circuit (a) results in V IR1 IR2 I ( R1 R2 ) (1) Likewise when applied to circuit (b), the equation becomes V IReq (2) In both circuits V and I are the same and it can be shown that Req R1 R2 (3) If there are more than 2 resistors then Req equals the sum of all the resistances in the circuit. Req R1 R2 ....... (4) (b) In parallel circuit connection, there are two or more paths for current to flow. Figure 2 shows such a circuit. I1 R1 I2 R2 I3 R3 Req I I + V - + V - (b) (a) Figure 2 A 3-resistors Parallel Circuit Kirchhoff’s Current Law when applied to circuit (a) results in I I1 I 2 I 3 V V V R1 R2 R3 (5) Likewise when applied to circuit (b), the same equation becomes I V Req (6) In both circuits V and I are the same and it can be shown that 1 1 1 1 Req R1 R2 R3 (7) Conductance G is defined as the reciprocal of the resistance G 1 R (8) Re-writing equation (7) in terms of conductances one obtains Geq G1 G2 G3 (9) It can be seen that the total conductance of resistors in parallel is equal to the summation of individual conductance of the resistors. Note that when more resistors are connected in parallel the total resistance to current flow from voltage source decreases. II. Experimental Work Materials required: A digital Multimeter (DMM), resistors 390Ω, 680Ω, 820Ω, 1kΩ, 1.2kΩ, and 2.2kΩ. (A) Series Connected Resistances Construct the following series circuits shown in Figure 3. R1 (i) A (ii) A (iii) B 390Ω 1kΩ R1 R3 R4 820Ω 1kΩ R6 B 390Ω R1 A R4 390Ω 2.2kΩ R2 R3 R4 680Ω 820Ω 1kΩ R5 R6 B 1.2kΩ 2.2kΩ Figure 3 Experimental Series Circuits 1. Measure the resistance of each resistor by an Ohmmeter and record the measured values in Table I. 2. Construct the circuit in Figure 3 (i) and measure the equivalent resistance between points A and B with an Ohmmeter. Record the measured value in Table I. 3. Calculate the equivalent resistance between points A and B from the measured values in part 1 and record this value in Table I. 4. Repeat steps 2-3 for circuits (ii) and (iii). Table I Series Resistance Measurements Measured Resistances Series Circuit R1 R2 R3 R4 R5 R6 Calculated Req Measured Req % Error (i) (ii) (iii) Answer the following questions: 1. Why did you use the measured values of the resistors in calculating R eq.? Why not use the colour-coded value? 2. Did your calculated value for Req equal your measured Req value? Explain any differences. 3. Would there be any difference in Req if the position of any resistor were changed in the circuit? 4. What would be the equivalent resistance measured if one of the resistors is removed in series circuits? What do we call such circuits? (B) Parallel Connected Resistances Construct the following parallel circuits. R1 390Ω (i) A B R2 1.2kΩ R1 1.2kΩ (ii) A B R2 1.2kΩ R1 390Ω R2 (iii) A B 620Ω R3 1.2kΩ Figure 4 Experimental Parallel Circuits 1. For each circuit measure the equivalent resistance between points A and B with an Ohmmeter. Record the measured value in Table II. 2. Calculate the equivalent resistance between points A and B for each circuit from the measured values in part A1, and record in Table II. Table II. Parallel Resistance Measurements Measured Resistances Parallel Circuit Calculated Req R1 R2 R3 % Error Measured Req (i) (ii) (iii) Answer the following questions: 1. How did the calculated values of Req and the measured Req compare? Explain any differences. Which Req is more accurate and why? 2. What relationship does Req have to the smallest parallel resistor in each experimental circuit? 3. Figure 4 circuit (ii) has 2 resistors of equal value in parallel. The result of your measurement should suggest a general rule for Req of any two parallel-connected resistors of the same value? What is this rule? 4. What do you think Req would be if there were 3 equal resistors in parallel? 5. How can you measure the resistance of an individual resistor in a parallel circuit? 6. What is the least number of resistances that can be used to create a parallel circuit? 7. If the lights on your New Year tree are wired in series, what will happen when one bulb burns out? What will happen if the bulbs are wired in parallel?