Twelve cells,each having emf E volts,are conn | vedclass

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(D) Let $m$ be the number of cells in the $12$-cell battery that are wrongly connected. Each wrongly connected cell cancels the emf of one correctly c

Vedclass · Accepted Answer

$1$

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(D) Let $m$ be the number of cells in the $12$-cell battery that are wrongly connected. Each wrongly connected cell cancels the emf of one correctly connected cell. Thus,the effective emf of the $12$-cell battery is $(12 - m)E - mE = (12 - 2m)E$.When the $12$-cell battery and the $2$-cell battery aid each other,the total emf in the circuit is $(12 - 2m)E + 2E = (14 - 2m)E$. The current is given by $i_1 = \frac{(14 - 2m)E}{R} = 3 	ext{ A}$ ... $(i)$.When they oppose each other,the total emf in the circuit is $(12 - 2m)E - 2E = (10 - 2m)E$. The current is given by $i_2 = \frac{(10 - 2m)E}{R} = 2 	ext{ A}$ ... (ii).Dividing equation $(i)$ by equation (ii),we get:$\frac{3}{2} = \frac{14 - 2m}{10 - 2m}$$3(10 - 2m) = 2(14 - 2m)$$30 - 6m = 28 - 4m$$2 = 2m$$m = 1$.Therefore,the number of wrongly connected cells is $1$.

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