Question

Derive the equation for resultant resistance of resistors in parrallel

Answer 1

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• Parallel combination of Resistors •

Imagine 3 resistors , R1 , R2 and R3 connected in series.

The current in these 3 resistors will be different ,, say ( I1 , I2 and I3 ) and total current through battery ( I )

=> I = I1 + I2 + I3

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

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

Let equivalent resistance be ( Re )

=> Re = V / I => I = V / Re

=> V / Re = V/ R1 + V / R2 + V / R3

♦ => 1 / Re = 1 / R1 + 1 / R2 + 1 / R3

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