Question

Two conductors are made of the same material and have the same length. Conductor $ A $ is a solid wire of diameter $ 1.0\, mm $ and conductor $ B $ is a hollow tube of outside diameter $ 2.0 \,mm $ and inside diameter $ 1.0\, mm $ . Find the resistance ratio $\frac {R_{A}} {R_{B}} $ measured between their ends

• A. 3
• B. 2
• C. 1
• D. 0.5

Answer 1

Answer: (A)

Resistance of wire, $R_{A}=\frac{\rho l}{A}=\frac{\rho l}{\pi\left[\frac{D}{2}\right]^{2}}=\frac{\rho l}{\frac{\pi D^{2}}{4}}$
$=\frac{\rho l}{\pi\frac{\left(1\right)^{2}}{4}}=\frac{4\rho l}{\pi}$
Similarly, for hollow conductor $B$
$R_{B}=\frac{\rho l}{A}=\frac{\rho l}{\pi\left[\frac{D_{1}^{2}}{4}-\frac{D_{2}^{2}}{4}\right]}=\frac{\rho l}{\pi\left[\frac{2^{2}}{4}-\frac{1^{2}}{4}\right]}$
$=\frac{4}{3} \frac{\rho l}{\pi}$
$\therefore \frac{R_{A}}{R_{B}}=\frac{4\rho l}{\pi}\times\frac{3\pi}{4\rho l}=3$