A coil of inductance 1, H and resistance 10, | vedclass

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

Question

(C) The rate at which magnetic energy is stored in the coil is given by $P_m = \frac{d}{dt}(\frac{1}{2}Li^2) = Li \frac{di}{dt}$.The rate at which ene

Vedclass · Accepted Answer

$0.36$

Vedclass · Answer

(C) The rate at which magnetic energy is stored in the coil is given by $P_m = \frac{d}{dt}(\frac{1}{2}Li^2) = Li \frac{di}{dt}$.The rate at which energy is supplied by the battery is $P_b = Ei$.The ratio of these rates is $\frac{P_m}{P_b} = \frac{Li \frac{di}{dt}}{Ei} = \frac{L}{E} \frac{di}{dt}$.For an $RL$ circuit,the current at time $t$ is $i = \frac{E}{R}(1 - e^{-Rt/L})$.The rate of change of current is $\frac{di}{dt} = \frac{E}{R} \cdot \frac{R}{L} e^{-Rt/L} = \frac{E}{L} e^{-Rt/L}$.Substituting this into the ratio expression:$\frac{P_m}{P_b} = \frac{L}{E} \left( \frac{E}{L} e^{-Rt/L} ight) = e^{-Rt/L}$.Given $R = 10\, \Omega$,$L = 1\, H$,and $t = 0.1\, s$:$\frac{P_m}{P_b} = e^{-(10 	imes 0.1) / 1} = e^{-1} \approx \frac{1}{2.718} \approx 0.368 \approx 0.36$.

$A$ coil of inductance $1\, H$ and resistance $10\, \Omega$ is connected to a battery of $emf$ $50\, V$ and negligible internal resistance at time $t = 0.$ The ratio of the rate at which magnetic energy is stored in the coil to the rate at which energy is supplied by the battery at $t = 0.1\, s$ is:

Similar Questions

In the circuit shown in the figure, what is the value of $I_1$ just after pressing the key $K$?

The dimensions of the "time constant" $\frac{L}{R}$ during the growth and decay of current in an inductive circuit are the same as those of:

The current in the $2\, \Omega$ resistance shown in the figure is:
$(a)$ Just after the closing of the key.
$(b)$ $A$ long time after the closing of the key.

Vedclass Test Series

Exam Paper Generator

Online Exam Module