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Electric Current> A cell of emf e and internal resistance r...

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A cell of emf e and internal resistance r supplies currents for the same time tthrough external resistances R1 and R2 respectively. If the heat produced in both the cases is the same, then the internal resistance is

Harsh kumar , 6 Years ago

Grade 10

1 Answers

Eshan

Last Activity: 6 Years ago

Dear student,

Current in a circuit of resistance $R$ and internal resistance $r$ is $I=\dfrac{E}{R+r}$
Power dissipated through the resistor= $I^2R=\dfrac{E^2R}{(R+r)^2}$

Hence heat dissipated= $I^2Rt=\dfrac{E^2R}{(R+r)^2}t$

Since the power dissipated is same in both cases,

$\dfrac{E^2R_1}{(R_1+r)^2}t=\dfrac{E^2R_2}{(R_2+r)^2}t$
$\implies r=\sqrt{R_1R_2}$

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