Question

In the circuit shown below, the ac source has voltage \(V = 30cos(ωt)\) volt with \(ω = 2000\) rad/s. What will be the amplitude of the current?

• A. \(\sqrt{5}\) A
• B. \(\frac{3}{\sqrt{5}}\) A
• C. \(3\) A
• D. \(3.3\) A

Hint:

Find X_L and X_C. They turn out to be equal, so the impedance equals the total resistance of 10 ohm.

Answer 1

The Correct Option is C

Step 1: Spot resonance first
Compute $\omega^2LC=(2000)^2\times5\times10^{-3}\times50\times10^{-6}=4\times10^6\times2.5\times10^{-7}=1$.

Step 2: What resonance means
$\omega^2LC=1$ means $X_L=X_C$, so the inductor and capacitor voltages cancel and the impedance equals the total resistance, $10\ \Omega$.

Step 3: Current
$I_0=\frac{30\ \text{V}}{10\ \Omega}=3$ A. Option (C).

Final Answer:
Amplitude of current is 3 A. \[ \boxed{3\ \text{A}} \]