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# $50V$ battery is supplying a current of $10A$ when connected to a resistor. If the efficiency of the battery at this current is 25%, then the internal resistance is:

$\begin {array} {1 1} (A)\;2.5\Omega & \quad (B)\;3.75\Omega \\ (C)\;1.25\Omega & \quad (D)\;5\Omega \end {array}$

This question requires the concept of efficiency used in the maximum power theorem.
$50 = 10 (R + r) \Rightarrow R + r = 5$
$\eta = \large\frac{R}{R+r}=$ $0.25$
$\large\frac{R}{5}=$ $0.25$
R=1.25
On solving the above set of equations, $r = 3.75\: ohms$
Ans : (B)

edited Sep 10, 2014