A coil of wire having finite inductance and r | vedclass

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

Question

(D) Let $k_1, k_2, k_3, k_4, k_5$ be constants.The current in the $RL$ circuit is given by $I_1(t) = k_1(1 - e^{-t/	au})$.The magnetic field $B(t)$ a

Vedclass · Accepted Answer

Passes through a maximum

Vedclass · Answer

(D) Let $k_1, k_2, k_3, k_4, k_5$ be constants.The current in the $RL$ circuit is given by $I_1(t) = k_1(1 - e^{-t/	au})$.The magnetic field $B(t)$ at the axis of the coil is proportional to the current $I_1(t)$,so $B(t) = k_2 I_1(t) = k_2 k_1(1 - e^{-t/	au})$.The induced current $I_2(t)$ in the ring is proportional to the rate of change of magnetic flux,which is proportional to $dB(t)/dt$. Thus,$I_2(t) = k_3 \frac{dB(t)}{dt} = k_4 e^{-t/	au}$.Therefore,the product $I_2(t) B(t) = k_5 (1 - e^{-t/	au}) e^{-t/	au} = k_5 (e^{-t/	au} - e^{-2t/	au})$.At $t = 0$,$I_2(t) B(t) = 0$. As $t 	o \infty$,$I_2(t) B(t) 	o 0$. Since the product is positive for $t > 0$,it must pass through a maximum.

Similar Questions

The current in the given circuit is increasing at a rate of $\frac{dI}{dt} = 4 \, A/s$. The charge on the capacitor at an instant when the current in the circuit is $2 \, A$ will be: ...... $\mu C$

The dimension of the ratio of magnetic flux and the resistance is equal to that of:

The network shown in the figure is part of a complete circuit. If at a certain instant the current $i$ is $5 \, A$ and is decreasing at the rate of $10^3 \, A/s$, then $V_B - V_A$ is: (in $ \, V$)

$A$ conducting wire frame is placed in a magnetic field which is directed into the paper. The magnetic field is increasing at a constant rate. The directions of induced currents in wires $AB$ and $CD$ are

An electron is moving in a circular orbit of radius $R$ with an angular acceleration $\alpha$. At the centre of the orbit is kept a conducting loop of radius $r$ $(r \ll R)$. The $e.m.f.$ induced in the smaller loop due to the motion of the electron is

Vedclass Test Series

Exam Paper Generator

Online Exam Module