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Question
Explain with the help of a labelled circuit diagram, how you will find the resistance of a combination of three resistors of resistances R1, R2 and R3 joined in parallel.
Solution
Let the resistance of the three resistors be R1, R2 and R3, respectively. Let their combined resistance be R. Let the total current flowing in the circuit be I and the strength of the battery be V. Then from Ohm's law, we have:
V = IR .....(1)
We know that when the resistors are connected in parallel, the potential drop across each resistance is the same.
Therefore:
I = I1 + I2 + I3
I = V/R1 + V/R2 + V/R3
I = V/(1/R1 + 1/R2 + 1/R3) ...... (2)
From equations (1) and (2) we have:
1/R = 1/R1 + 1/R2 + 1/R3
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