Question 246: AC fundamentals

Question

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

Accepted Answer

Step 1: Recall key concepts
True power (P)
= $ V I \cos \phi$
Apparent power (S)
= $ V I$
Power factor (p.f.)
= $ \dfrac{P}{S} = \cos \phi$
So, the ratio of true power to apparent power is
$\cos \phi$
.
Step 2: Express $\cos \phi$ in terms of $R$ and $Z$
For a series $RLC$ circuit:
Impedance magnitude: $ Z = \sqrt{R^2 + (X_L - X_C)^2}$
Phase angle: $	an \phi = \dfrac{X_L - X_C}{R}$
Therefore, $\cos \phi = \dfrac{R}{Z}$
Step 3: Compare with answer choices
Option A. $ 	frac{Z}{R} $ Ã¢ÂÂ reciprocal, not correct.
Option B. $ 	an \phi $ Ã¢ÂÂ not correct.
Option C. $ \cot \phi $ Ã¢ÂÂ not correct.
Option D.
$ 	frac{R}{Z} $
Ã¢ÂÂ matches $\cos \phi$. Ã¢ÂÂ
Ã¢ÂÂ Final Answer:
$ 	ext{The ratio of true power to apparent power is } \frac{R}{Z}. $
Correct option: D

Answer

$\frac{\mathrm{Z}}{\mathrm{R}}$

Answer

$ 	an \phi$

Answer

$\cot \phi$

Answer

$\frac{R}{Z}$

AC fundamentals

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

Choose the correct answer: