Alternating Current

JEE Main level, single correct, medium

129 of 190

Question 129 of 190


As shown in the figure, a battery of emf ∈\in is connected to an inductor LL and resistance RR in series. The switch is closed at t=0.t=0. The total charge that flows from the battery, between t=0t=0 and t=tct={t}_{c} ( tc{t}_{c} is the time constant of the circuit) is:

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Answer: (A) ∈LeR2\dfrac{\in L}{e{R}^{2}}

q=∫0Tcidtq=\int _{0}^{{T}_{c}}idt
=∈R[t−e−tTc−1Tc]0Tc=∈R[Tc+Tce−1−Tc]=\dfrac{\in }{R}{\left[t-\dfrac{{e}^{-\dfrac{t}{{T}_{c}}}}{-\dfrac{1}{{T}_{c}}}\right]}_{0}^{{T}_{c}} =\dfrac{\in }{R}\left[{T}_{c}+{T}_{c}{e}^{-1}-{T}_{c}\right]
=∈R×1e×LR=\dfrac{\in }{R}\times \dfrac{1}{e}\times \dfrac{L}{R}
q=∈LR2eq=\dfrac{\in L}{{R}^{2}e}

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