(B) The current in an $LR$ circuit at time $t$ is given by the formula: $I(t) = I_0(1 - e^{-\frac{R}{L}t})$.We are given that the current reaches $\fr

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(B) The current in an $LR$ circuit at time $t$ is given by the formula: $I(t) = I_0(1 - e^{-\frac{R}{L}t})$.We are given that the current reaches $\frac{e-1}{e}$ of its final value $I_0$.So,$I(t) = \left(\frac{e-1}{e}\right)I_0 = I_0(1 - e^{-1})$.Comparing this with the formula,we get $e^{-\frac{R}{L}t} = e^{-1}$.This implies $\frac{R}{L}t = 1$,or $t = \frac{L}{R}$.Given $L = 60\, H$ and $R = 30\, \Omega$,we have $t = \frac{60}{30} = 2\, s$.

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

Difficult

$A$ 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?

A
$1$
B
$2$
C
$e$
D
$2e$

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Electromagnetic Induction

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R-L D.C. Circuit

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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In the circuit shown,$X$ is joined to $Y$ for a long time,and then $X$ is joined to $Z$. The total heat produced in $R_2$ is:

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Switch $S$ of the circuit shown in the figure is closed at $t = 0$. If $e$ denotes the induced $emf$ in $L$ and $i$ the current flowing through the circuit at time $t$,which of the following graphs is correct?

Medium

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Regarding the given circuit,the correct statement is:

MediumAP EAMCET 2023

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An $L-R$ circuit has a cell of $e.m.f.$ $E$,which is switched on at time $t = 0$. The current in the circuit after a long time will be

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$A$ 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

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?

In the circuit shown,$X$ is joined to $Y$ for a long time,and then $X$ is joined to $Z$. The total heat produced in $R_2$ is:

Switch $S$ of the circuit shown in the figure is closed at $t = 0$. If $e$ denotes the induced $emf$ in $L$ and $i$ the current flowing through the circuit at time $t$,which of the following graphs is correct?

Regarding the given circuit,the correct statement is:

An $L-R$ circuit has a cell of $e.m.f.$ $E$,which is switched on at time $t = 0$. The current in the circuit after a long time will be

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