In an LR circuit connected to a battery,the r | vedclass

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

Question

(A) The energy stored in an inductor is given by $U = \frac{1}{2} LI^2$.The rate at which energy is stored is the power $P = \frac{dU}{dt} = LI \left(

Vedclass · Accepted Answer

Vedclass · Answer

(A) The energy stored in an inductor is given by $U = \frac{1}{2} LI^2$.The rate at which energy is stored is the power $P = \frac{dU}{dt} = LI \left( \frac{dI}{dt} ight)$.For an $LR$ circuit,the current at time $t$ is $I(t) = I_0 (1 - e^{-Rt/L})$,where $I_0 = \frac{E}{R}$ is the maximum current.The rate of change of current is $\frac{dI}{dt} = \frac{I_0 R}{L} e^{-Rt/L}$.Substituting these into the power equation:$P = L \left[ I_0 (1 - e^{-Rt/L}) ight] \left[ \frac{I_0 R}{L} e^{-Rt/L} ight] = I_0^2 R (e^{-Rt/L} - e^{-2Rt/L})$.At $t = 0$,$I = 0$,so $P = 0$.As $t 	o \infty$,$\frac{dI}{dt} 	o 0$,so $P 	o 0$.Since the rate is zero at both $t = 0$ and $t = \infty$ and positive in between,the curve must start from zero,rise to a maximum,and return to zero.

In an $LR$ circuit connected to a battery,the rate at which energy is stored in the inductor is plotted against time during the growth of current in the circuit. Which of the following best represents the resulting curve?

Similar Questions

In the given circuit,when does the lamp become momentarily bright?

$A$ long straight wire is parallel to one edge of a rectangular loop as shown in the figure. If the current in the long wire varies with time as $I = I_0 e^{-t/\tau}$,what will be the induced $emf$ in the loop?

$A$ conducting loop having a capacitor is moving outward from the magnetic field. Which plate of the capacitor will be positive?

The current $i$ in a coil varies with time as shown in the figure. The variation of induced $emf$ with time would be

Vedclass Test Series

Exam Paper Generator

Online Exam Module