State the law of combination of resistances in parallel.

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Solution

In a parallel combination, the voltage remains the same across each resistor but the current gets divided. Let I₁_, I₂ and I₃ be the current across resistors R₁_,R₂ and R₃, respectively.
I = I₁ + I₂+ I₃
V = IR, V = I₁R₁, V = I₂R₂, V = I₃R₃
$I = \frac{V}{R}, I_{1} = \frac{V}{R_{1}}, I_{2} = \frac{V}{R_{2}}, I_{3} = \frac{V}{R_{3}} Using these values, we get : \frac{V}{R} = \frac{V}{R_{1}} + \frac{V}{R_{2}} + \frac{V}{R_{3}} \frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}$
So, the total resistance is the sum of the reciprocal of the individual resistances.

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