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WBJEE · Physics · Current Electricity

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

  1. A \(\frac{I_{0}}{\lambda}\)
  2. B \(\frac{2 I_{0}}{\lambda}\)
  3. C \(I_{0} \lambda\)
  4. D \(e^{I_{0}\lambda}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{I_{0}}{\lambda}\)

Step-by-step Solution

Detailed explanation

The current \(1=1_{0} e^{-x}\) is of exponential nature. \(I=\frac{d Q}{d t}=I_{0} e^{-\lambda t}\) \(d Q=I_{0} e^{-\lambda t} d t\) \(\int_{0}^{Q} d Q=I_{0} \int_{t=0}^{t=-\infty} e^{-\lambda t} \cdot d t\) \(Q=I_{0} \times \frac{1}{\lambda}=\frac{I_{0}}{\lambda}\)