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Grade 10Electric Current

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

Harsh kumar

8 Years agoGrade 10

1 Answer

Eshan

8 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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