Question

The mass of a wire of resistance 20 ohm is 50 gram. The resistance of the same wire of mass 10 gram is

• A. 4$\Omega$
• B. 5$\Omega$
• C. 100$\Omega$
• D. 80$\Omega$

Answer 1

Answer: (A)

4$\Omega$

$m_1=50m_2=10$

$L_1{A}_1=50;L_2{A}_2=10$

$\frac{L_1}{L_2}\left(\frac{A_1}{A_2}\right)=5\rho L_1=20A_1$

$\frac{R_1}{R_2}=\frac{20}{R_2}=\left(\frac{L_1}{A_1}\right)\left(\frac{A_2}{L_2}\right)$

As the wire is same [assuming it has same area of cross section]

$\Rightarrow \frac{m_1}{m_2}=\frac{L_1}{L_2}$

$5=\frac{L_1}{L_2}$

$L_2=\frac{L_1}{5}$

$\Rightarrow R_2=\frac{\rho L_2}{A_2}=\frac{20}{5}=4\Omega$