Question

An inductor of reactance \(100\) \(\Omega\), a capacitor of reactance \(50\) \(\Omega\), and a resistor of resistance \(50\) \(\Omega\) are connected in series with an AC source of \(10\) V, \(50\) Hz. Average power dissipated by the circuit is ____

• A. \(1\) W
• B. \(2\) W
• C. \(3\) W
• D. \(4\) W

Hint:

Average power is $I_{rms}^2R$ with $Z=\sqrt{R^2+(X_L-X_C)^2}$.

Answer 1

The Correct Option is A

Step 1: Impedance
\(X_L-X_C=100-50=50\,\Omega\) and \(R=50\,\Omega\). \(Z=\sqrt{50^2+50^2}=50\sqrt2\,\Omega\).

Step 2: Current
Taking \(10\) V as the rms voltage, \(I=\frac{10}{50\sqrt2}=\frac{1}{5\sqrt2}\) A.

Step 3: Power
\(P=I^2R=\frac{1}{50}\times50=1\) W. Option (A).

Final Answer:
The average power is \(1\) W, option (A). \[ \boxed{\text{(A) }1\text{ W}} \]