Question

In an AC circuit containing L, C, R in series, the ratio of true power to apparent power is

• A. $Z/R$
• B. $\tan \phi$
• C. $\cot \phi$
• D. $R/Z$

Hint:

Power Factor ($\cos \phi$) = Resistance Impedance.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question asks for the definition of the power factor of an AC circuit.

Step 2: Detailed Explanation:
1. True power (\( P_{\text{avg}} \)) is given by \( V_{\text{rms}} I_{\text{rms}} \cos \phi \).
2. Apparent power is the product \( V_{\text{rms}} I_{\text{rms}} \).
3. The ratio of true power to apparent power is \( \cos \phi \), which is called the power factor.
4. From the impedance triangle, \( \cos \phi = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{R}{Z} \).

Step 3: Final Answer:
The ratio is \( \frac{R}{Z} \).