Question

derive an expression for the total resistance of three resistances connected in parallel​

Answer 1

Heya Mate...........................

Here is your answer............................

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Take 3 resistance R1, R2 and R3 connected in parallel and connect a battery of V volts. In this case the p.d across the end will be the same. The resistance flowing, is not same.

Total I = I1+I2+I3 ______(1)

From ohm's law

I = V/R_______(2)

I1 = V/R1______(3)

I2 = V/R2______(4)

I3 = V/R3_______(5)

putting values of I1, I2 and I3 in eq (1)

V/R = V/R1 + V/R2 + V/R3

= V/R = V[1/R1 + 1/R2 + 1/R3]

= 1/R = 1/R1 + 1/R2 + 1/R3    ( Hence Proved)

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Thanks........................