A cell supplies a current $i_{1}$ through a resistance $R_{1}$ and a current $i_{2}$ through a resistance $R_{2}$ . The internal resistance of this cell is

R_{2} - R_{1}

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\frac{i_{1} R_{2} - i_{2} R_{1}}{i_{1} - i_{2}}

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\frac{i_{2} R_{2} - i_{1} R_{1}}{i_{1} - i_{2}}

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(\frac{i_{1} + i_{2}}{i_{1} - i_{2}}) \sqrt{R_{1} R_{2}}

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Solution

The correct option is C $\frac{i_{2} R_{2} - i_{1} R_{1}}{i_{1} - i_{2}}$
Let the emf of the cell be $E$

Current in the circuit, $i = \frac{E}{r + R}$

Current in the circuit when resistance $R_{1}$ and $R_{2}$ are connected (separately) respectively

$i_{1} = \frac{E}{r + R_{1}}$ -------(1)

$i_{2} = \frac{E}{r + R_{2}}$ -------(2)

From these two equations, we get

$i_{1} (r + R_{1})$ = $i_{2} (r + R_{2})$

$\Rightarrow r (i_{1} - i_{2}) = i_{2} R_{2} - i_{1} R_{1}$

$\Rightarrow r$ = $\frac{i_{2} R_{2} - i_{1} R_{1}}{i_{1} - i_{2}}$

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Resistance

Standard IX Physics

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