A constant voltage is applied between two end | vedclass

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

Question

(A) The rate of heat developed in a wire is given by the power formula: $P = \frac{V^2}{R}$.Initially,the resistance of the wire is $R_1 = \frac{\rho

Vedclass · Accepted Answer

Increased $8$ times

Vedclass · Answer

(A) The rate of heat developed in a wire is given by the power formula: $P = \frac{V^2}{R}$.Initially,the resistance of the wire is $R_1 = \frac{\rho L}{A} = \frac{\rho L}{\pi r^2}$.Thus,the initial power is $P_1 = \frac{V^2}{R_1}$.When the length is halved $(L' = L/2)$ and the radius is doubled $(r' = 2r)$,the new resistance $R_2$ becomes:$R_2 = \frac{\rho (L/2)}{\pi (2r)^2} = \frac{\rho L / 2}{\pi (4r^2)} = \frac{\rho L}{8 \pi r^2} = \frac{R_1}{8}$.The new power $P_2$ is given by:$P_2 = \frac{V^2}{R_2} = \frac{V^2}{R_1 / 8} = 8 \left( \frac{V^2}{R_1} \right) = 8 P_1$.Therefore,the rate of heat developed increases $8$ times.

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

Similar Questions

$A\, 5\, ^oC$ rise in the temperature is observed in a conductor by passing some current. When the current is doubled,then the rise in temperature will be equal to ............. $^oC$.

The heat developed in an electric wire of resistance $R$ by a current $I$ for a time $t$ is

When two electric bulbs of $40\, W$ and $60\, W$ are connected in parallel,then:

It takes $12$ minutes to boil $1$ litre of water in an electric kettle. Due to some defect, it becomes necessary to remove $20\%$ of the turns of the heating coil of the kettle. After repair, how much time will it take to boil $1$ litre of water?

Two electric bulbs have ratings $P_1 \text{ watt}, V \text{ volt}$ and $P_2 \text{ watt}, V \text{ volt}$. If they are connected in parallel to a $V \text{ volt}$ supply,the total power consumed will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module