First slide

Cell

Question

'Two sources of equal e.m.f, are connected to an external resistance .R. The internal resistances of the two sources are R₁, and R₂ (R₂ >R₁) If the potential difference across the source having internal resistance .R₂, is zero, then

Moderate

A

R = R₂ - R₁,
B

$R = \frac{R_{1} R_{2}}{R_{2} - R_{1}}$
C

$R = \frac{R_{1} R_{2}}{R_{1} + R_{2}}$
D

$R = R_{2} [\frac{R_{1} + R_{2}}{R_{2} - R_{1}}]$

Solution

The current flowing through the circuit is given by
$i = \frac{2 E}{R + R_{1} + R_{2}}$
Potential difference across the source of internal resistance R₂ is given by
$G I V E N v_{2} = E - i R_{2} = 0$ $E = \frac{2 E R_{2}}{R + R_{1} + R_{2}}$
or $R + R_{1} + R_{2} = 2 R_{2} or R = R_{2} - R_{1}$

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