The heater of an electric kettle is made of a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The resistance of the original wire is $R = \rho \frac{L}{A} = \rho \frac{L}{\pi (d/2)^2} = \frac{4 \rho L}{\pi d^2}$.The power consumed is $P = \

Vedclass · Accepted Answer

$(B, D)$

Vedclass · Answer

(A) The resistance of the original wire is $R = ho \frac{L}{A} = ho \frac{L}{\pi (d/2)^2} = \frac{4 ho L}{\pi d^2}$.The power consumed is $P = \frac{V^2}{R}$. The time taken to heat the water is $t = 4 	ext{ minutes}$.For the new wires,each has length $L$ and diameter $2d$. The resistance of each new wire is $R' = ho \frac{L}{\pi (d)^2} = \frac{ho L}{\pi d^2} = \frac{R}{4}$.If the two new wires are connected in series,the equivalent resistance is $R_s = R' + R' = 2R' = \frac{R}{2}$.The power in series is $P_s = \frac{V^2}{R_s} = \frac{V^2}{R/2} = 2P$. Since $P \propto 1/t$,the time taken is $t_s = \frac{t}{2} = \frac{4}{2} = 2 	ext{ minutes}$.If the two new wires are connected in parallel,the equivalent resistance is $R_p = \frac{R' 	imes R'}{R' + R'} = \frac{R'}{2} = \frac{R/4}{2} = \frac{R}{8}$.The power in parallel is $P_p = \frac{V^2}{R_p} = \frac{V^2}{R/8} = 8P$. The time taken is $t_p = \frac{t}{8} = \frac{4}{8} = 0.5 	ext{ minutes}$.Thus,$(B)$ and $(D)$ are correct.

Similar Questions

When an electric heater is switched on, the current flowing through it $(I)$ is plotted against time $(t)$. Taking into account the variation of resistance with temperature, which of the following best represents the resulting curve?

The $emf$ of a thermocouple, with one junction kept at $0^{\circ}C$, is given by the equation $e = at + bt^2$. The Peltier coefficient is given by:

Two heaters $A$ and $B$ have power ratings of $1 \text{ kW}$ and $2 \text{ kW}$,respectively. These two are first connected in series and then in parallel to a fixed power source. The ratio of power outputs for these two cases is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module