Question

Two wires ‘A’ and ‘B’ of the same material have their lengths in the ratio 1 : 2 and radii in the ratio 2 : 1. The two wires are connected in parallel across a battery. The ratio of the heat produced in ‘A’ to the heat produced in ‘B’ for the same time is

• A. 1 : 2
• B. 2 : 1
• C. 1 : 8
• D. 8 : 1

Answer 1

Answer: (D)

8 : 1

Answer 2

Resistance $R = \rho\frac{l}{\pi r^{2}} \Rightarrow R \propto \frac{l}{r^{2}}$ ⇒ $\frac{R_{A}}{R_{B}} = \frac{l_{A}}{l_{B}} \times \left( \frac{r_{B}}{r_{A}} \right)^{2}$

⇒ $\frac{R_{A}}{R_{B}} = \frac{1}{2} \times \left( \frac{1}{2} \right)^{2} = \frac{1}{8}$

By using $H = \frac{V^{2}t}{R} \Rightarrow \frac{H_{A}}{H_{B}} = \frac{R_{B}}{R_{A}} = \frac{8}{1}$