Question

We have two wires A and B of same mass and same material. The diameter of the wire A is half of that B. If the resistance of wire A is 24 ohm then the resistance of wire B will be

• A. 12 ohm
• B. 3.0 ohm
• C. 1.5 ohm
• D. None of the above

Answer 1

Answer: (C)

1.5 ohm

Same material $\to$ same density, specific resistance as they are material property.

$R=\frac{pl}{A}=\frac{pv}{A^2}=\frac{pm}{d{A}^2}$

$R\propto \frac{1}{A^2}\propto \frac{1}{r^4}$

$\frac{R_A}{R_B}=\frac{r_B^4}{r_A^4}=2^4=16\Rightarrow R_B=\frac{24}{16}=1.5\Omega$