Resistors are sometimes joined together and they have several applications in electronics. Obtain the expression for the effective resistance in the combination of two resistors $R_{1}$ and $R_{2}$ in parallel.

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Solution

When two resistor are connected in parallel, they will have common terminals A and B as shown in figure. Thus, there is same potential V across each resistor.
In parallel , $I = I_{1} + I_{2}$
or $\frac{V}{R_{e f f}} = \frac{V}{R_{1}} + \frac{V}{R_{2}}$ (by Ohm's law)
$\frac{1}{R_{e f f}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$
or $R_{e f f} = \frac{R_{1} R_{2}}{R_{1} + R 2}$

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