An alternating voltage $e = 150\sqrt{2}sin100t$ volt is applied to a capacitor of capacity $2 μ\text{F}$. The root mean square value of current in the circuit is

Question

In an a.c. circuit, voltage and current are given by: \[ V = 100 \sin(100t) \, \text{V} \quad \text{and} \quad I = 100 \sin\left(100t + \frac{\pi}{3}\right) \, \text{mA}. \] The average power dissipated in one cycle is:

Answer 1

Step 1: Peak Current First:
$I_0=\omega CV_0=100\times2\times10^{-6}\times150\sqrt2=0.03\sqrt2$ A.

Step 2: Convert:
$I_{rms}=\dfrac{I_0}{\sqrt2}=0.03$ A $=30$ mA.

Step 3: Answer:
Option (C).

Final Answer:
Option (C). \[ \boxed{\text{(C) } 30\ \text{mA}} \]

An alternating voltage \(e = 150\sqrt{2}sin100t\) volt is applied to a capacitor of capacity \(2 μ\text{F}\). The root mean square value of current in the circuit is

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The Correct Option is C

Solution and Explanation

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