(C) In an $LR$ circuit, when a $DC$ voltage $V$ is applied, the current $I$ at any time $t$ is given by the equation $I(t) = \frac{V}{R}(1 - e^{-Rt/L}

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$A$ resistor and an inductor in series

(C) In an $LR$ circuit, when a $DC$ voltage $V$ is applied, the current $I$ at any time $t$ is given by the equation $I(t) = \frac{V}{R}(1 - e^{-Rt/L})$.Initially, at $t = 0$, the current is $I = 0$ because the inductor opposes the change in current.As time $t$ increases, the current gradually rises and approaches a steady-state value of $I_{max} = \frac{V}{R}$ as $t \to \infty$.This behavior matches the description provided in the question.Therefore, the circuit contains a resistor and an inductor in series.

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

Easy

When a $DC$ voltage is applied at the two ends of a circuit kept in a closed box, it is observed that the current gradually increases from zero to a certain value and then remains constant. What do you think the circuit contains?

WBJEE 2020 All WBJEE

A
$A$ resistor alone
B
$A$ capacitor alone
C
$A$ resistor and an inductor in series
D
$A$ resistor and a capacitor in series

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Electromagnetic Induction

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R-L D.C. Circuit

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Two resistors of $10 \Omega$ and $20 \Omega$ and an ideal inductor of $10 \ H$ are connected to a $2 \ V$ battery as shown. The key $K$ is closed at time $t=0$. Find the initial $(t=0)$ and final $(t \rightarrow \infty)$ currents through the battery.

Medium

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In an $L-R$ circuit,for the case of increasing current,the magnitude of current can be calculated by using the formula:

Easy

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$A$ 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 $, s$)

MediumAIEEE 2005

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$A$ coil of resistance $50 \Omega$ is connected across a $5.0 V$ battery. If the current in the coil is found to be $50 mA$ after the time $t=0.1 s$ of the battery being connected, then the inductance of the coil is:

MediumTS EAMCET 2021

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In the given figure,an inductor of $L = 4 \, H$ and a resistor of $R = 25 \, \Omega$ are connected in series with a battery of emf $E$ volt. $\frac{E^a}{2b} \, J/s$ represents the maximum rate at which energy is stored in the magnetic field of the inductor. The numerical value of $\frac{b}{a}$ is ............

DifficultJEE MAIN 2023

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When a $DC$ voltage is applied at the two ends of a circuit kept in a closed box, it is observed that the current gradually increases from zero to a certain value and then remains constant. What do you think the circuit contains?

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Two resistors of $10 \Omega$ and $20 \Omega$ and an ideal inductor of $10 \ H$ are connected to a $2 \ V$ battery as shown. The key $K$ is closed at time $t=0$. Find the initial $(t=0)$ and final $(t \rightarrow \infty)$ currents through the battery.

In an $L-R$ circuit,for the case of increasing current,the magnitude of current can be calculated by using the formula:

$A$ 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 resistance $50 \Omega$ is connected across a $5.0 V$ battery. If the current in the coil is found to be $50 mA$ after the time $t=0.1 s$ of the battery being connected, then the inductance of the coil is:

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