A solenoid has an inductance of 60 , H and a | vedclass

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

Question

(B) The current in an $LR$ circuit at time $t$ is given by the formula $I(t) = I_0(1 - e^{-t/	au})$,where $I_0 = V/R$ is the maximum steady-state cur

Vedclass · Accepted Answer

$2 \, s$

Vedclass · Answer

(B) The current in an $LR$ circuit at time $t$ is given by the formula $I(t) = I_0(1 - e^{-t/	au})$,where $I_0 = V/R$ is the maximum steady-state current and $	au = L/R$ is the time constant of the circuit.We are asked to find the time $t$ when the current reaches $\frac{e-1}{e} \approx 63.2\%$ of its final value $I_0$.This condition corresponds to $I(t) = I_0(1 - e^{-1}) = I_0(1 - 1/e)$.Comparing this with the general formula $I(t) = I_0(1 - e^{-t/	au})$,we see that $t = 	au$.The time constant $	au$ is calculated as $	au = \frac{L}{R} = \frac{60 \, H}{30 \, \Omega} = 2 \, s$.Therefore,it will take $2 \, s$ for the current to reach approximately $63.2\%$ of its final value.

$A$ solenoid has an inductance of $60 \, H$ and a resistance of $30 \, \Omega$. If it is connected to a $100 \, V$ battery,how long will it take for the current to reach $\frac{e-1}{e} \approx 63.2\%$ of its final value?

Similar Questions

Find the current in the sliding rod $AB$ (resistance $= R$) for the arrangement shown in the figure. The magnetic field $\vec{B}$ is constant and directed out of the paper. The parallel wires have no resistance,and the velocity $v$ is constant. The switch $S$ is closed at time $t = 0$.

In the figure,a lamp $P$ is in series with an iron-core inductor $L$. When the switch $S$ is closed,the brightness of the lamp rises relatively slowly to its full brightness compared to the case without the inductor. This is due to:

$A$ coil of inductance $300\, mH$ and resistance $2\, \Omega$ is connected to a source of voltage $2\, V$. The current reaches half of its steady state value in $t$ seconds. Find the value of $t$. (in $, s$)

$A$ coil of inductance $8.4 \, mH$ and resistance $6 \, \Omega$ is connected to a $12 \, V$ battery. The current in the coil is $1.0 \, A$ at approximately the time

$A$ 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

Vedclass Test Series

Exam Paper Generator

Online Exam Module