Question

An alternating voltage \(V=200\sqrt{2}\sin (100t)\) volt is connected to \(1\ \mu F\) capacitor through a.c. ammeter. The reading of ammeter is

• A. \(5\ \text{mA}\)
• B. \(10\ \text{mA}\)
• C. \(15\ \text{mA}\)
• D. \(20\ \text{mA}\)

Hint:

An a.c. ammeter shows the rms current. Find the rms voltage and the capacitive reactance, then divide.

Answer 1

The Correct Option is D

Step 1: Peak Current
$I_{0}=V_{0}\omega C=200\sqrt{2}\times100\times10^{-6}=0.02\sqrt{2}\ \text{A}$.

Step 2: RMS Value
$I_{rms}=\frac{I_{0}}{\sqrt{2}}=0.02\ \text{A}$.

Step 3: Convert
$0.02\ \text{A}=20\ \text{mA}$.

Final Answer:
The reading is 20 mA. \[ \boxed{\text{(D) }20\ \text{mA}} \]