Question

The effective $\frac{6}{5}\Omega$. When two wires are joined in parallel. When one of the wire breaks, the effective resistance is 2 ohms. The resistance of the broken wire was:-

• A. $\frac{3}{5}\Omega$
• B. $2\Omega$
• C. $3\Omega$
• D. $5\Omega$

Answer 1

The correct option is C $3\Omega$

Two resistors $R_1$ & $R_2$ are joined in parallel and their equivalent

resistance is $R^{\prime }=\frac{6}{5}\Omega$ [consider wines an resistance]

In parallel :-

$\Rightarrow R^{\prime }=\frac{R_1{R}_2}{R_1+R_2}=\frac{6}{5}\Omega \to \left(1\right)$

Suppose $R_1$ breaks. Hence only $R_2$ contribution to resistance

$\Rightarrow R_2=2\Omega$

Put $R_2$ back in (1),

$\Rightarrow \frac{2R_1}{R_1+2}=\frac{6}{5}\Rightarrow R_1=3\Omega$ ans