Question

Determine the value of resistance $R$ in the circuit shown in the figure, when the current is zero in the branch $CD$.

• A. $10\Omega$
• B. $50\Omega$
• C. $20\Omega$
• D. $40\Omega$

Answer 1

The correct option is D $40\Omega$

We can observe that the points $A$ and $E$ are at same potential, similarly the points $B$ and $F$ are at same potential because they are lying on same conducting wire.


Thus, the four resistances $5\Omega ,R,20\Omega ,10\Omega$ forms the four arms of a wheatstone bridge and resistance connected across $CD$ forms the diagonal arm.

$\Rightarrow$The current in the branch $CD$ can be zero only if the potential difference across $CD$ is zero.

$\text{Or},V_C=V_D$

Thus the wheatstone bridge should be balanced.

$\Rightarrow 5\times R=20\times 10$

$\therefore R=\frac{200}{5}=40\Omega$