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# For what value of $R$ will the current passing through the $4\: ohm$ resistor is zero

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

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)

edited Sep 10, 2014