Consider a parallel combination of the cells | vedclass

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(A) Let $V$ be the potential difference between points $B_1$ and $B_2$,such that $V = V_{B_2} - V_{B_1}$.For the two cells in parallel,the currents $I

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$V = \varepsilon_{eq} - Ir_{eq}$

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(A) Let $V$ be the potential difference between points $B_1$ and $B_2$,such that $V = V_{B_2} - V_{B_1}$.For the two cells in parallel,the currents $I_1$ and $I_2$ flowing through them are given by:$I_1 = \frac{\varepsilon_1 - V}{r_1}$ and $I_2 = \frac{\varepsilon_2 - V}{r_2}$.The total current $I$ is the sum of these currents:$I = I_1 + I_2 = \frac{\varepsilon_1 - V}{r_1} + \frac{\varepsilon_2 - V}{r_2}$.Rearranging the terms to solve for $V$:$I = \left( \frac{\varepsilon_1}{r_1} + \frac{\varepsilon_2}{r_2} \right) - V \left( \frac{1}{r_1} + \frac{1}{r_2} \right)$.$V \left( \frac{r_1 + r_2}{r_1 r_2} \right) = \left( \frac{\varepsilon_1 r_2 + \varepsilon_2 r_1}{r_1 r_2} \right) - I$.$V = \left( \frac{\varepsilon_1 r_2 + \varepsilon_2 r_1}{r_1 + r_2} \right) - I \left( \frac{r_1 r_2}{r_1 + r_2} \right)$.Comparing this with the equation for a single equivalent cell,$V = \varepsilon_{eq} - Ir_{eq}$,we see that the potential difference is indeed $V = \varepsilon_{eq} - Ir_{eq}$.

Consider a parallel combination of the cells shown in the figure. The potential difference between $B_1$ and $B_2$ is

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