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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

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

Grade:10

1 Answers

Eshan
askIITians Faculty 2095 Points
2 years ago
Dear student,

Current in a circuit of resistanceRand internal resistancerisI=\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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