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A current $I=I_{0} e^{-\lambda t}$ is flowing in a circuit consisting of a parallel combination of resistance $R$ and capacitance $C$. The total charge over the entire pulse period is
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The correct answer is:
$\frac{I_{0}}{\lambda}$
The current $1=1_{0} e^{-x}$ is of exponential nature.
$I=\frac{d Q}{d t}=I_{0} e^{-\lambda t}$
$d Q=I_{0} e^{-\lambda t} d t$
$\int_{0}^{Q} d Q=I_{0} \int_{t=0}^{t=-\infty} e^{-\lambda t} \cdot d t$
$Q=I_{0} \times \frac{1}{\lambda}=\frac{I_{0}}{\lambda}$
$I=\frac{d Q}{d t}=I_{0} e^{-\lambda t}$
$d Q=I_{0} e^{-\lambda t} d t$
$\int_{0}^{Q} d Q=I_{0} \int_{t=0}^{t=-\infty} e^{-\lambda t} \cdot d t$
$Q=I_{0} \times \frac{1}{\lambda}=\frac{I_{0}}{\lambda}$
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