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Question

Two cells of internal resistances $$r_1$$ and $$r_2$$ and of same emf are connected in series, across a resistor of resistance R. If the terminal potential difference across the cells of internal resistance $$r_1$$ is zero, then the value of R is?


A
R=2(r1+r2)
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B
R=r2r1
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C
R=r1r2
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D
R=2(r1r2)
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Solution

The correct option is A $$R=r_1-r_2$$
$$E^1=2E;$$
$$R^1=r_1+r_2+R; I=\dfrac{2E}{r_1+r_2+R}$$
$$V=E-Ir_1=0$$
$$\Rightarrow E=\dfrac{2E r_1}{r_1+r_2+R}\Rightarrow 2r_1=r_1+r_2+R\Rightarrow R=r_1-r_2$$.

Physics

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