What is the equivalent resistance across A and B in the figure shown, if $R = 3 Ω$ ?

9 Ω

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12 Ω

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15 Ω

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8 Ω

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Solution

The correct option is C $8 Ω$
$R_{1} = R_{2} = R_{3} = R_{4} = R_{5} = R$
$R^{'}$ and $R_{2}$ are in series
Their equivalent resistance,
$R^{'} = R_{1} + R_{2} = 2 R$
Now $R^{'}$ and $R_{3}$ in are parallel
Their equivalent resistance $R "$ is given by
$\frac{1}{R "} = \frac{1}{R^{'}} + \frac{1}{R_{3}} = \frac{1}{2 R} + \frac{1}{R}$
$\frac{1}{R "} = \frac{1 + 2}{2 R}$
$R "= \frac{2 R}{3}$
$R ", R_{5} & R_{4}$ are in series
$∴ R_{f} = R " + R_{5} + R_{4} = 2 R + 2 R / 3 = 8 R / 3$ ,
Since $R = 3 Ω$
$∴ R_{f} = 8 \times \frac{3}{3} = 8 Ω$ .

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