A cell of emf E and internal resistance r supplies currents for the same time t through external resistances R 1 = 100 Ω and R 2 = 40 Ω separately. If the heat developed in both cases is the same, then the internal resistance of the cell is

Question

A cell of emf E and internal resistance r supplies currents for the same time t through external resistances R 1 = 100 Ω and R 2 = 40 Ω separately. If the heat developed in both cases is the same, then the internal resistance of the cell is, 28.6 Ω, 80 Ω, 63.3 Ω, 140 Ω

MARKS App · Accepted Answer

Current drawn from the cell in resistance R 1 will be I = E R 1 + r . Therefore, heat produced in R 1 will be H 1 = E 2 R 1 t R 1 + r 2 . Heat produced in R 2 will be H 2 = E 2 R 2 t R 2 + r 2 . As per question, H 1 = H 2 E 2 R 1 t R 1 + r 2 = E 2 R 2 t R 2 + r 2 On solving we get, r = R 1 R 2 = 100 × 40 = 63.25 Ω

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