An inductor of inductance L = 400 mH and res | vedclass

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

Question

(D) When the switch $S$ is closed at $t = 0$,the branch containing $R_1$ is in parallel with the branch containing $L$ and $R_2$. The potential differ

Vedclass · Accepted Answer

$12e^{-5t} \ V$

Vedclass · Answer

(D) When the switch $S$ is closed at $t = 0$,the branch containing $R_1$ is in parallel with the branch containing $L$ and $R_2$. The potential difference across the $L-R_2$ branch is equal to the emf of the battery,$E = 12 \ V$.The current $i$ in the $L-R_2$ branch grows according to the equation: $i = \frac{E}{R_2}(1 - e^{-R_2 t / L})$.The potential drop across the inductor $L$ is given by $V_L = L \frac{di}{dt}$.Differentiating the current expression with respect to time $t$:$\frac{di}{dt} = \frac{E}{R_2} \cdot \frac{R_2}{L} e^{-R_2 t / L} = \frac{E}{L} e^{-R_2 t / L}$.Substituting this into the expression for $V_L$:$V_L = L \left( \frac{E}{L} e^{-R_2 t / L} ight) = E e^{-R_2 t / L}$.Given $E = 12 \ V$,$R_2 = 2 \ \Omega$,and $L = 400 \ mH = 0.4 \ H$,the time constant $	au = \frac{L}{R_2} = \frac{0.4}{2} = 0.2 \ s$.Thus,$V_L = 12 e^{-t / 0.2} = 12 e^{-5t} \ V$.

Similar Questions

$A$ coil of inductance $5\,H$ is joined to a cell of $emf$ $6\,V$ through a resistance $10\,\Omega$ at time $t = 0$. The $emf$ across the coil at time $t = \ln \sqrt{2}\,s$ is:....$V$

The figure shows a circuit containing three resistors ($9 \ \Omega$ each) and two inductors ($4 \ mH$ each). The reading of the ammeter at the moment the switch $K$ is turned $ON$ is $...... \ A$.

For the given circuit,the current $i$ through the battery when the key is closed and the steady state has been reached is .....$A$.

If $R$ and $L$ denote resistance and inductance respectively,which of the following has the dimension of time?

An inductance coil has a time constant of $4 \, sec$. If it is cut into two equal parts and connected in parallel,then the new time constant of the circuit is.....$sec$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module