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Q.

If same heat is produced when a resistor $R_{1}$ is connected to a battery for a given time as it is produced in resistor $R_{2}$ in the same time, then the internal resistance of the battery is

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a

$\frac{R_{1} + R_{2}}{2}$

b

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

c

$\sqrt{R_{1} (R_{1} + R_{2})}$

d

$\sqrt{R_{1} R_{2}}$

answer is D.

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Detailed Solution

$\frac{E^{2}}{{(R_{1} + r)}^{2}} R_{1} t = \frac{E^{2}}{{(R_{2} + r)}^{2}} R_{2} t$

$r = \sqrt{R_{1} R_{2}}$

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If same heat is produced when a resistor R1 is connected to a battery for a given time as it is produced in resistor R2 in the same time, then the internal resistance of the battery is