Four cells, each of emf E and internal resist | vedclass

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(A) When four cells of emf $E$ are connected in series, the total emf is $4E$. If one cell is connected in reverse, its emf opposes the others. Theref

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$\frac{2 E}{4 r+R}$

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(A) When four cells of emf $E$ are connected in series, the total emf is $4E$. If one cell is connected in reverse, its emf opposes the others. Therefore, the effective emf of the circuit is $E_{eff} = E + E + E - E = 2E$. The total internal resistance of the four cells in series is $r_{total} = r + r + r + r = 4r$. The total resistance of the circuit is $R_{total} = 4r + R$. Using Ohm's law, the current $I$ in the external circuit is given by $I = \frac{E_{eff}}{R_{total}} = \frac{2E}{4r + R}$.

Four cells, each of emf $E$ and internal resistance $r$, are connected in series across an external resistance $R$. By mistake, one of the cells is connected in reverse. Then the current in the external circuit is

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