Question

A heater of 220 V heats a volume of water in 5 minute time. A heater of 110 V heats the same volume of water in

• A. 5 minutes
• B. 8 minutes
• C. 10 minutes
• D. 20 minutes

Answer 1

Answer: (D)

20 minutes

Answer 2

By using $H = \frac{V^{2}t}{R}.$ Here volume of water is same. So same heat is required in both cases. Resistance is also constant so V²t = constant

⇒$t \propto \frac{1}{V^{2}}$

⇒ $\frac{t_{1}}{t_{2}} = \left( \frac{V_{2}}{V_{1}} \right)^{2} \Rightarrow \frac{5}{t_{2}} = \left( \frac{110}{220} \right)^{2} = \frac{1}{4} \Rightarrow t_{2} = 20\min$