$\begin {array} {1 1} (A)\;1\Omega & \quad (B)\;2\Omega \\ (C)\;3\Omega & \quad (D)\;4\Omega \end {array}$

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Potential difference across the $ 4\: ohm$ resistor is zero $ \Rightarrow$ potential difference across

$2\: ohm $ resistor is $4V$ and across $R$ will $-2V$.

The current through the 2 ohm resistor is 2A.

The KVL equation for the big loop is

10 - 2i -iR - 4 = 0

On solving the $KVL$ equations, we get $ R = 1 \: ohm$.

Ans : (A)

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