First slide

Equivalent of battery

Question

48 cells each of internal resistance $1 Ω$ are arranged in a mixed combination and the combination is connected across a resistor of resistance $3 Ω$ . Number of cells in each row is n and number of rows is m if maximum current flows through the $3 Ω$ resistor, then

Difficult

A

$m = 3, n = 6$
B

$m = 4, n = 12$
C

$m = 8, n = 6$
D

$m = 2, n = 24$

Solution

$m n = N .... (1) and for maximum current, mR=Nr ...... (2)$
From (1) and (2), $m = \sqrt{\frac{N r}{R}} = \sqrt{\frac{48 \times 1}{3}} = 4 a n d n = \frac{48}{4} = 12$

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