Question

In a series LCR circuit alternating e.m.f. and current are given by the equations \(V = V_0sin(ωt)\) and \(I = I_0sin(ωt+\frac{π}{3})\) respectively. The average power dissipated in the circuit over one cycle of a.c. is \((cos60^{\circ} = 0.5)\)

• A. zero
• B. \(\frac{V_0I_0}{2}\)
• C. \(\frac{\sqrt{3}}{2}V_0I_0\)
• D. \(\frac{V_0I_0}{4}\)

Hint:

At resonance the reactances cancel, so the circuit behaves as a pure resistance.

Answer 1

The Correct Option is D

Step 1: Phase angle:
$\tan\phi = \frac{X_L - X_C}{R} = 0$ at resonance, so $\phi = 0$.

Step 2: Meaning:
Zero phase angle means that current and voltage reach their peaks together. So (D).

Final Answer:
Option (D). \[ \boxed{\text{(D)}} \]