Four identical cells, each of EMF E and internal resistance r , are connected first in series and then in parallel across an external resistor R . If the value of the external resistance is R = 2r , the ratio of the current in the series combination to the current in the parallel combination ( I_s : I_p ) is:

Step-by-step solution

For the series combination of 4 identical cells, the equivalent EMF is 4E and the equivalent internal resistance is 4r . The current in the series circuit is: I_s = 4E 4r + R = 4E 4r + 2r = 4E 6r = 2E 3r For the parallel combination of 4 identical cells, the equivalent EMF remains E and the equivalent internal resistance is r 4 . The current in the parallel circuit is: I_p = E r 4 + R = E r 4 + 2r = E 9r 4 = 4E 9r The ratio of the currents is: I_s I_p = 2E 3r 4E 9r = 2 3 9 4 = 3 2 Thus, the ratio is 3:2 . Answer: 3