Question

derivation of parralel series​

Answer 1

3 resistances R1, R2 and R3 connected in parallel between A and B. Let V be the pot. diff. applied across the combination.

Let I1, I2 and I3 be the currents through the resistances R1, R2 and R3 respectively. Then the current in the main circuit must be I = I1 + I2 + I3

​Since, all the resistances have been connected between the same two points A and B, therefore, potential drop V is same across each of them. By Ohm's law, the currents through the individual resistances will be

I1 = V/R1, I2= V/R2, I3 = V/R3

​If Rp is the resistance of teh parallel combination, then we must have

I = V/Rp

​But, I = I1+ I2 + I3

​or V/Rp = V/R1+ V/R2 + V/R3

or 1/Rp = 1/R1 + 1/R2 + 1/R3

Answer 2

Your answer is here

Source-Lakhmir Singh and Manjit

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