For the two cells having same EMF E and internal resistance r, the current passing through the external resistor 6 Ω is same when both the cells are connected either in parallel or in series. The value of internal resistance r i $s _______$ Ω.
Options

Question

For the two cells having same EMF E and internal resistance r, the current passing through the external resistor 6 Ω is same when both the cells are connected either in parallel or in series. The value of internal resistance r i $s _______$ Ω.

Options

G1 Physics · Accepted Answer

When the two identical cells are connected in series, equivalent emf = 2E, equivalent internal resistance = 2r. Therefore, I(series) = 2E/(6+2r). When the two identical cells are connected in parallel, equivalent emf = E, equivalent internal resistance = r/2. Hence, I(parallel) = E/(6+r/2). The currents are equal: 2E/(6+2r) = E/(6+r/2). Cancel E: 2/(6+2r) = 1/(6+r/2). Cross-multiplying, 12+r = 6+2r. Therefore, r = 6 Ω. Correct option: D.

For the two cells having same EMF E and internal resistance r, the current passing through the external resistor 6 Ω is same when both the cells are connected either in parallel or in series. The value of internal resistance r i s _______ Ω.