First slide

Equivalent of battery

Question

A set of n equal resistors, of value R each, are connected in series to a battery of emf E and internal resistance R. The current drawn is I. Now, the n resistors are connected in parallel to the same battery. Then the current drawn from battery becomes 10I. The value of n is

Moderate

A

10
B

11
C

20
D

9

Solution

Current drawn from a battery when n resistors are connected in series is
$I = \frac{E}{n R + R} . . . . . . . (i)$
Current drawn from same battery when n resistors are connected in parallel is
$10 I = \frac{E}{\frac{R}{n} + R} . . . . . . . . . (i i)$
$On dividing eqn. (ii) by (i), 10 = \frac{(n + 1) R}{(\frac{1}{n} + 1) R}$
After solving the equation, n=10

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