Question

An alternating voltage given as, \(E=100\sqrt{2}\sin (100t)\) volt is applied to a capacitor of \(1\ \mu \text{F}\). The current reading of the ammeter will be equal to

• A. \(20\ \text{mA}\)
• B. \(10\ \text{mA}\)
• C. \(40\ \text{mA}\)
• D. \(80\ \text{mA}\)

Hint:

Find the capacitive reactance, divide the rms voltage by it, and remember an AC ammeter shows the rms current.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
From \(E=E_{0}\sin\omega t\): \(E_{0}=100\sqrt{2}\ \text{V}\) and \(\omega=100\ \text{rad/s}\). An AC ammeter reads the rms current.

Step 2: Calculation
Capacitive reactance \(X_{C}=\frac{1}{\omega C}=\frac{1}{100\times 10^{-6}}=10^{4}\ \Omega\). \(E_{rms}=\frac{100\sqrt{2}}{\sqrt{2}}=100\ \text{V}\).

Step 3: Compare the options
\(I_{rms}=\frac{E_{rms}}{X_{C}}=\frac{100}{10^{4}}=10^{-2}\ \text{A}=10\ \text{mA}\), which is the second option.

Final Answer:
The ammeter reads \(10\ \text{mA}\). \[ \boxed{\text{(B) }10\ \text{mA}} \]