A constant voltage is applied between the two | vedclass

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

Question

(A) The rate of heat developed (power) in a wire is given by $P = \frac{V^2}{R}$, where $V$ is the constant voltage and $R$ is the resistance.Since $R

Vedclass · Accepted Answer

Will be doubled

Vedclass · Answer

(A) The rate of heat developed (power) in a wire is given by $P = \frac{V^2}{R}$, where $V$ is the constant voltage and $R$ is the resistance.Since $R = \rho \frac{l}{A} = \rho \frac{l}{\pi r^2}$, we have $P \propto \frac{1}{R} \propto \frac{r^2}{l}$.Let the initial length be $l_1 = l$ and radius be $r_1 = r$. Then $P_1 \propto \frac{r^2}{l}$.When both length and radius are doubled, $l_2 = 2l$ and $r_2 = 2r$.The new power is $P_2 \propto \frac{r_2^2}{l_2} = \frac{(2r)^2}{2l} = \frac{4r^2}{2l} = 2 \left( \frac{r^2}{l} \right)$.Therefore, $P_2 = 2P_1$. The rate of heat developed will be doubled.

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

Similar Questions

In a large building,there are $15$ bulbs of $40\ W$,$5$ bulbs of $100\ W$,$5$ fans of $80\ W$,and $1$ heater of $1\ kW$. The voltage of the electric mains is $220\ V$. The minimum capacity of the main fuse of the building will be ................ $A$.

$A$ resistor dissipates $192 \, J$ of energy in $1 \, s$ when a current of $4 \, A$ is passed through it. Now,when the current is doubled,the amount of thermal energy dissipated in $5 \, s$ is $..... \, J$.

If a $2\, kW$ boiler is used everyday for $1$ hour, then the electrical energy consumed by the boiler in thirty days is .......... $units$.

$A$ resistor develops $500 \, J$ of thermal energy in $20 \, s$ when a current of $1.5 \, A$ is passed through it. If the current is increased from $1.5 \, A$ to $3 \, A$,what will be the energy (in $J$) developed in $20 \, s$?

An electric kettle takes $4 \ A$ current at $220 \ V$. If the entire electric energy is converted into heat energy, then the time (in minutes) taken to increase the temperature of $1 \ kg$ of water from $34^{\circ} C$ to $100^{\circ} C$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module