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

Regarding the given circuit,the correct statement is:

The time taken for the magnetic energy to reach $25\%$ of its maximum value,when a solenoid of resistance $R$ and inductance $L$ is connected to a battery,is:

$Henry/ohm$ can be expressed in

$A$ series $L-R$ circuit is connected to a battery of emf $V$. If the circuit is switched on at $t = 0$,then the time at which the energy stored in the inductor reaches $\left(\frac{1}{n}\right)$ times of its maximum value,is

$A$ coil of inductance $0.20 \, H$ is connected in series with a switch and a cell of $emf$ $1.6 \, V$. The total resistance of the circuit is $4.0 \, \Omega$. What is the initial rate of growth of the current when the switch is closed? (in $A \, s^{-1}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module