Question

Water boils in an electric kettle in 15 minutes after switching on. If the length of the heating wire is decreased to 2/3 of its initial value, then the same amount of water will boil with the same supply voltage in

• A. 15 minutes
• B. 12 minutes
• C. 10 minutes
• D. 8 minutes

Answer 1

Answer: (C)

10 minutes

Answer 2

By using $H = \frac{V^{2}t}{R}$ where $R = \rho\frac{l}{A} \Rightarrow H = \frac{V^{2}tA}{\rho l}$. Since volume is constant so H is also constant so t ∝ l which gives $\frac{t_{2}}{t_{1}} = \frac{l_{2}}{l_{1}}$ ⇒ $\frac{t_{2}}{15} = \frac{\frac{2}{3}l_{1}}{l_{1}} \Rightarrow t_{2} = 10\min$