Question

Two wires have their lengths, diameters and resistivities in the ratio of $1:2$. If the resistance of the thinner wire is $10\Omega$, the resistance of the thicker wire is ________.

• A. $5\Omega$
• B. $10\Omega$
• C. $20\Omega$
• D. $40\Omega$

Answer 1

The correct option is B $10\Omega$

Resistance of the wire $R=\rho \frac{l}{A}$

where $A=\frac{\pi d^2}{4}$

$⟹\frac{R_2}{R_1}=\frac{{\rho }_2}{{\rho }_1}\frac{l_2}{l_1}\frac{d_1^2}{d_2^2}$

$\therefore$ $\frac{R_2}{10}=\frac{1}{2}\times \frac{1}{2}\times \frac{2^2}{1^2}=1$

$⟹R_2=10\Omega$