Question

In an a.c. circuit containing L, C and R in series, the ratio of apparent power to the true power is
(Z= impedance of the circuit and R= resistance )

• A. \(RZ\)
• B. \(cosφ\)
• C. \(cotφ\)
• D. \(\frac{Z}{R}\)

Hint:

True power = V I cos phi, apparent power = V I, and cos phi = R/Z.

Answer 1

The Correct Option is D

Step 1: Use the power triangle:
Apparent power $S$, true power $P$ and reactive power $Q$ form a right triangle with $\cos\phi=\dfrac PS$.

Step 2: Invert:
$\dfrac SP=\dfrac{1}{\cos\phi}=\dfrac ZR$.

Step 3: Pick:
Option D.

Final Answer:
Apparent over true power is 1/cos phi, which equals Z/R. \[ \boxed{\text{(D) }\dfrac ZR} \]