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: Understanding the Concept
The ammeter reads \(I_{rms}=\frac{V_{rms}}{X_{C}}\) with \(X_{C}=\frac{1}{\omega C}\).

Step 2: Voltage
\(V_{0}=200\sqrt{2}\ \text{V}\), so \(V_{rms}=\frac{V_{0}}{\sqrt{2}}=200\ \text{V}\). Also \(\omega=100\ \text{rad/s}\).

Step 3: Reactance
\(X_{C}=\frac{1}{100\times10^{-6}}=10^{4}\ \Omega\).

Step 4: Current
\(I_{rms}=\frac{200}{10^{4}}=0.02\ \text{A}=20\ \text{mA}\).

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