Two cells A and B of electromotive forces 1.3 V and 1.5 V, respectively, are arranged as shown in figure. The voltmeter (assumed ideal reads 1.45 V, the internal resistances of cells A and B are $r_{A} a n d r_{B},$ respectively. Which of the following is correct?

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$r_{A} = 2 r_{B}$

$r_{A} = 3 r_{B}$

$r_{B} = 2 r_{A}$

$r_{B} = 3 r_{A}$

answer is B.

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Detailed Solution

$1.45 + 1.3 + I r_{A}$

$1.45 = 1.5 - I r_{B}$

$I r_{B} - 0.05$

Dividing, we get $\frac{r_{B}}{r_{A}} = \frac{1}{3}$

Or $r_{A} = 3 r_{B}$

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