In a network as shown in the figure the potential difference across the resistance 2R (the cell has an emf of E and has no internal resistance) :-

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\frac{4 E}{7}

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\frac{E}{7}

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Solution

The correct option is B $\frac{4 E}{7}$
Total resistance of circuit is $R_{t} = R + \frac{2 R .4 R}{2 R + 4 R} = \frac{7 R}{3}$
Current in the circuit is $I = \frac{E}{R_{t}} = 3 E / 7 R$
Potential across R is $V_{1} = I R = 3 E / 7$
As R and (2R, 4R) are in series so potential across (2R,4R) is $V_{2} = E - V_{1} = E - 3 E / 7 = 4 E / 7$ . This is also potential across 2R because 2R and 4R are in parallel.

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