A cell of constant emf is first connected to a resistance R1 and then connected to a resistance R2 . If power delivered in both cases is equal, then the internal resistance of the cell is

A cell of constant emf is first connected to a resistance R₁ and then connected to a resistance R₂ . If power delivered in both cases is equal, then the internal resistance of the cell is

A
$\sqrt{R_{1} R_{2}}$
B
$\sqrt{\frac{R_{1}}{R_{2}}}$
C
$\frac{R_{1} - R_{2}}{2}$
D
$\frac{R_{1} + R_{2}}{2}$

Solution:

$i = \frac{E}{r + R} & P = i^{2} R G i v e n, P_{1} = P_{2} \Rightarrow {(\frac{E}{r + R_{1}})}^{2} R_{1} = {(\frac{E}{r + R_{2}})}^{2} R_{2} \Rightarrow r = \sqrt{R_{1} R_{2}}$

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