(B) In an $LR$ circuit,the current $I$ at time $t$ is given by the equation $I(t) = I_0(1 - e^{-t/\tau})$,where $I_0$ is the maximum steady-state curr

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Reaches a value equal to about $63\%$ of its final value

(B) In an $LR$ circuit,the current $I$ at time $t$ is given by the equation $I(t) = I_0(1 - e^{-t/\tau})$,where $I_0$ is the maximum steady-state current and $\tau = L/R$ is the time constant.When $t = \tau$,the current becomes $I(\tau) = I_0(1 - e^{-1})$.Since $e^{-1} \approx 0.368$,we have $I(\tau) = I_0(1 - 0.368) = I_0(0.632)$.This means the current reaches approximately $63\%$ of its final maximum value.

Class 12 Physics Electromagnetic Induction R-L D.C. Circuit

Easy

The time constant of an $LR$ circuit represents the time in which the current in the circuit

A
Reaches a value equal to about $37\%$ of its final value
B
Reaches a value equal to about $63\%$ of its final value
C
Attains a constant value
D
Attains $50\%$ of the constant value

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Electromagnetic Induction

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R-L D.C. Circuit

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MediumIIT 1999

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In the circuits $(a)$ and $(b)$,switches $S_1$ and $S_2$ are closed at $t = 0$ and are kept closed for a long time. The variations of current in the two circuits for $t \ge 0$ are roughly shown by which figure? (Figures are schematic and not drawn to scale.)

DifficultJEE MAIN 2015

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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:

MediumAIIMS 2018

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$A$ 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 $A \, s^{-1}$)

Medium

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In the circuit shown below,the key $K$ is closed at $t = 0$. The current through the battery is

DifficultAIEEE 2010

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The time constant of an $LR$ circuit represents the time in which the current in the circuit

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