Question

A wire of resistance ${10}^{-6}\Omega /m$ is bend in the form of a circle of diameter $2m$. If a wire of same material is connected across its diameter as shown in figure, then the total resistance across its diameter $AB$ will be

• A. $14\pi \times {10}^{-6}\Omega$
• B. $0.88\times {10}^{-6}\Omega$
• C. $\frac{2}{3}\pi \times {10}^{-6}\Omega$
• D. $\frac{4}{3}\pi \times {10}^{-6}\Omega$

Answer 1

The correct option is B $0.88\times {10}^{-6}\Omega$

Resistance across $AB$
$\frac{1}{R^{\prime }}=\frac{1}{R_0}+\frac{1}{R_1}+\frac{1}{R_2}$
Here, $R_1=\pi \times 1\times {10}^{-6}\Omega$
$R_1=\pi \times {10}^{-6}\Omega$
and $R_2=2\times {10}^{-6}\Omega$
$\therefore \frac{1}{R^{\prime }}=\frac{1}{\pi \times {10}^{-6}}+\frac{1}{\pi \times {10}^{-6}}+\frac{1}{2\times {10}^{-6}}$
$R^{\prime }=0.88\times {10}^{-6}C$.