Explanation

(d) $\frac{1}{R^{'}} = \frac{1}{10} + \frac{1}{10} + \frac{1}{20} \Rightarrow R^{'} = \frac{20}{5} = 4\ \Omega$
Now using ohm’s law $i = \frac{25}{R + R'} \Rightarrow 0.5 = \frac{25}{R + 4}$
$\Rightarrow R + 4 = \frac{25}{0.5} = 50 \Rightarrow R = 50 - 4 = 46\ \Omega$
Current through $20\Omega$ resistor $= \ \frac{0.5 \times 5}{20 + 5} = \frac{2.5}{25} = 0.1A$
Potential difference across middle resistor
= Potential difference across $20\Omega = 20 \times 0.1 = 2V$