Question

A constant voltage is applied between the two ends of a metallic wire. If both the length and the radius of the wire are doubled, the rate of heat developed in the wire will

• A. be halved
• B. be doubled
• C. remain the same
• D. be quadrupled

Answer 1

Answer: (B)

be doubled

We know that resistance $R=\frac{\rho L}{A}=\frac{\rho L}{\pi r^2}$ where $\rho =$resistivity, $L=$ length of wire and $A=\pi r^2$ cross sectional area.
Heat means the power across the wire.
Initial Heat is $P_i=\frac{V^2}{R}=\frac{V^2\pi r^2}{\rho L}$
when $L=2L,r=2r,P_f=\frac{V^2\pi \left(4r^2\right)}{\rho \left(2L\right)}=2\frac{V^2\pi r^2}{\rho L}=2P_i$