Question

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

• A. \(5\)
• B. \(10\)
• C. \(15\)
• D. \(20\)

Hint:

Find the capacitive reactance from the angular frequency and capacitance, then divide the rms voltage by it.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
A capacitor opposes alternating current with a capacitive reactance \(X_C=\frac{1}{\omega C}\). An AC ammeter reads the rms current \(I_{rms}=\frac{V_{rms}}{X_C}\).

Step 2: Read the data
From \(V=200\sqrt{2}\sin(100t)\): \(V_0=200\sqrt{2}\) V and \(\omega=100\) rad/s.
Also \(C=1\,\mu F=10^{-6}\) F.

Step 3: Calculation
\(V_{rms}=\frac{V_0}{\sqrt{2}}=200\) V.
\(X_C=\frac{1}{100\times10^{-6}}=10^{4}\,\Omega\).
\(I_{rms}=\frac{200}{10^{4}}=0.02\) A \(=20\) mA.

Step 4: Compare the options
The reading is 20 mA, which matches option (D).

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