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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.
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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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