A coil of inductance 300, mH and resistance 2 | vedclass

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

Question

(D) The current in an $LR$ circuit is given by $i = i_0(1 - e^{-Rt/L})$,where $i_0 = V/R$ is the steady state current.We are given that the current re

Vedclass · Accepted Answer

$0.1$

Vedclass · Answer

(D) The current in an $LR$ circuit is given by $i = i_0(1 - e^{-Rt/L})$,where $i_0 = V/R$ is the steady state current.We are given that the current reaches half of its steady state value,so $i = i_0/2$.Substituting this into the equation: $i_0/2 = i_0(1 - e^{-Rt/L})$.This simplifies to $1/2 = 1 - e^{-Rt/L}$,which means $e^{-Rt/L} = 1/2$.Taking the natural logarithm on both sides: $-Rt/L = \ln(1/2) = -\ln(2)$.Thus,$t = (L/R) \ln(2)$.Given $L = 300\, mH = 0.3\, H$ and $R = 2\, \Omega$,we have $t = (0.3 / 2) 	imes 0.693$.$t = 0.15 	imes 0.693 = 0.10395\, s \approx 0.1\, s$.

$A$ 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 $, s$)

Similar Questions

An ideal coil of $10 \ H$ is connected in series with a resistance of $5 \ \Omega$ and a battery of $5 \ V$. $2 \ s$ after the connection is made,the current flowing in the circuit in amperes is:

In an $L-R$ circuit,the current reaches $\frac{3}{4}$ of its maximum value in $4 \ s$. What is the time constant of the $L-R$ circuit?

An inductance $L$ and a resistance $R$ are first connected to a battery. After some time,the battery is disconnected,but $L$ and $R$ remain connected in a closed circuit. Then the current reduces to $37\%$ of its initial value in

$A$ constant voltage of $25 \, V$ is applied to a series $L-R$ circuit at $t=0$ by closing a switch. What is the potential difference across the resistor and the inductor at time $t=0$?

An emf of $15 V$ is applied to a circuit containing $5 H$ inductance and $10 \Omega$ resistance. The ratio of currents at time $t=\infty$ and $t=1 s$ after closing the switch is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module