Four identical cells, each of 2 , V e.m.f., a | vedclass

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(C) The equivalent e.m.f. of $n$ identical cells in parallel is $E_{eq} = E = 2 \, V$.The equivalent internal resistance of $n$ identical cells in par

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$7.5$

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(C) The equivalent e.m.f. of $n$ identical cells in parallel is $E_{eq} = E = 2 \, V$.The equivalent internal resistance of $n$ identical cells in parallel is $r_{eq} = \frac{r}{n} = \frac{r}{4}$.The external circuit consists of two $15 \, \Omega$ resistors in parallel, so the equivalent external resistance $R$ is:$R = \frac{15 	imes 15}{15 + 15} = \frac{225}{30} = 7.5 \, \Omega$.The terminal voltage $V$ is given by $V = I 	imes R$, where $I$ is the current in the circuit.$I = \frac{V}{R} = \frac{1.6}{7.5} \, A$.Using the terminal voltage equation $V = E_{eq} - I 	imes r_{eq}$:$1.6 = 2 - \left( \frac{1.6}{7.5} ight) 	imes \left( \frac{r}{4} ight)$.Rearranging to solve for $r$:$2 - 1.6 = \left( \frac{1.6}{7.5} ight) 	imes \left( \frac{r}{4} ight)$$0.4 = \frac{1.6 	imes r}{30}$$0.4 	imes 30 = 1.6 	imes r$$12 = 1.6 	imes r$$r = \frac{12}{1.6} = 7.5 \, \Omega$.

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