A source of constant voltage V is connected t | vedclass

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

Question

(A) Let $i$ be the current through the resistance $R$,and $i_1$ and $i_2$ be the currents through inductors $L_1$ and $L_2$ respectively.At $t=0$,the

Vedclass · Accepted Answer

$A, B, C$

Vedclass · Answer

(A) Let $i$ be the current through the resistance $R$,and $i_1$ and $i_2$ be the currents through inductors $L_1$ and $L_2$ respectively.At $t=0$,the inductors act as open circuits because the current cannot change instantaneously. Thus,the current through the resistance $R$ is $0$.For $t > 0$,the voltage across the parallel combination of $L_1$ and $L_2$ is the same. Therefore,$V_{L1} = V_{L2} \implies L_1 \frac{di_1}{dt} = L_2 \frac{di_2}{dt}$.Integrating both sides with respect to time,we get $L_1 i_1 = L_2 i_2$ (assuming initial currents are zero). This implies $\frac{i_1}{i_2} = \frac{L_2}{L_1}$,so the ratio of currents is fixed at all times.After a long time,the inductors act as short circuits (ideal inductors). The total current $i = \frac{V}{R}$.Since $i_1 + i_2 = i = \frac{V}{R}$ and $L_1 i_1 = L_2 i_2$,we have $i_2 = \frac{L_1}{L_2} i_1$.Substituting this into the current equation: $i_1 + \frac{L_1}{L_2} i_1 = \frac{V}{R} \implies i_1 \left( \frac{L_1+L_2}{L_2} \right) = \frac{V}{R} \implies i_1 = \frac{V}{R} \frac{L_2}{L_1+L_2}$.Similarly,$i_2 = \frac{V}{R} \frac{L_1}{L_1+L_2}$.Thus,options $A, B,$ and $C$ are correct.

Similar Questions

$A$ conducting ring of radius $a$ is rotated about a point $O$ on its periphery as shown in the figure in a plane perpendicular to a uniform magnetic field $B$ which exists everywhere. The rotational velocity is $\omega$. Choose the correct statement$(s)$ related to the induced current in the ring.

$A$ coil is placed in a magnetic field of $1 \, T$. Its area changes at a rate of $\frac{5 \, m^2}{ms}$. If the current in the coil changes from $1 \, A$ to $2 \, A$ in $2 \times 10^{-3} \, s$,what is the inductance of the coil in $H$?

The current $I$ through a coil varies with time $t$ as shown in the graph. Plot the graph for the induced $emf$ $e$ versus time $t$ for the coil.

$A$ square loop of side $2 \,cm$ enters a magnetic field with a constant speed of $2 \,cm \,s^{-1}$ as shown. The front edge enters the field at $t=0 \,s$. Which of the following graphs correctly depicts the induced emf in the loop? (Take clockwise direction as positive)

Vedclass Test Series

Exam Paper Generator

Online Exam Module