Postby **TGTS0907129**»
Resistors in parallel

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Suppose that a box contain a group of three resistors in parallel, of resistance R_{1}, R_{2} and R_{3}. the resistance of the combination will be R=V/I, where V is the voltage across the terminals of box and I is the total current in it. Since the voltage across each of the resistors is V, the voltage across the terminals of the box, the currents in the individual resistors are

I_{1} = V/R_{1} I_{2} = V/R_{2} I_{3} = V/R_{3}

The sum of these three currents must be the total current I, so that

I = I_{1} + I_{2} + I_{3}

or, I = V/R_{1} + V/R_{2} + V/R_{3}

This can be written

I = V(1/R_{1} + 1/R_{2} + 1/R_{3} )

or, I/V = V/R_{1} + V/R_{2} + V/R_{3}

Since V/I = R, we known that I/V = 1/R so that

I/R = V/R_{1} + V/R_{2} + V/R_{3}

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