Question

In the circuit shown, a metre bridge is in its balance state. The metre bridge wire has a resistance of $1\Omega {\text{cm}}^{-1}$. Calculate the value of unknown resistance $X$ if the battery has negligible internal resistance.

• A. $2\Omega$
• B. $4\Omega$
• C. $1\Omega$
• D. $3\Omega$

Answer 1

The correct option is A $2\Omega$

For balanced Wheatstone bridge,

$\frac{X}{40}=\frac{3}{60}$

$\Rightarrow X=2\Omega$

Hence, option (b) is correct answer.

Key concept: If a constant current flows through a wire of uniform area of cross-section, then potential drop along the wire is directly proportional to the length of the wire. We can compare these type of circuits with a balanced Wheatstone bridge, when no current flows through galvanometer. $\frac{R_1}{R_2}=\frac{R_3}{R_4}=\frac{\left(l\right)cm}{(100-l)cm}$