a circuit has resistance R is connected to an similar cell if the current in the circuit is the same whether the cells are connected in series or in parallel then the internal resistance R of each cell given by,?

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Samyak Jain · Answer

Case 1. Resistance R is connected to n similar cells each of internal resistance r and emf E in series. Equivalent emf of n identical cells in series = nE and equivalent resistance of the circuit = nr +R. Let current in the circuit be i 1 . By Ohm’s law, nE = i 1 (nr + R) i 1 = nE / (nr + R) ...(1). Case 2. Resistance R is connected to n similar cells each of internal resistance r and emf E. The cells are connected in parallel. Equivalent emf of n identical cells in parallel = E and equivalent resistance of the circuit = r/n +R. Let current in the circuit be i 2 . By Ohm’s law, E = i 2 (r/n + R) i 2 = E / (r/n + R) = nE / (r + nR) ...(2). It is given that i 1 = i 2 . From (1) and (2), nE / (nr +R) = nE / (r + nR) i.e. 1 / (nr +R) = 1 / (r + nR). nr + R = r + nR (n – 1)r = (n – 1)R r = R .

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a circuit has resistance R is connected to an similar cell if the current in the circuit is the same whether the cells are connected in series or in parallel then the internal resistance R of each cell given by,?

a circuit has resistance R is connected to an similar cell if the current in the circuit is the same whether the cells are connected in series or in parallel then the internal resistance R of each cell given by,?

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