Question

If the power factor changes from 0.5 to 0.25 because impedance changes from $Z_1$ to $Z_2$ then $Z_1 = x Z_2$. The value of x is (Resistance remains constant)

• A. 0.1
• B. 0.5
• C. 0.7
• D. 0.4

Hint:

Power factor is the ratio of real power to apparent power, or $R/Z$ in circuit terms.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The power factor in an AC circuit is given by the cosine of the phase angle, which can be expressed in terms of resistance ($R$) and impedance ($Z$).
Step 2: Key Formula or Approach:
Power Factor $\cos \phi = \frac{R}{Z}$.
Step 3: Detailed Explanation:
Let $R$ be the constant resistance.
For the first case:
$0.5 = \frac{R}{Z_1} \implies Z_1 = \frac{R}{0.5} = 2R$
For the second case:
$0.25 = \frac{R}{Z_2} \implies Z_2 = \frac{R}{0.25} = 4R$
The problem states $Z_1 = x Z_2$. Substituting the values:
\[ 2R = x (4R) \]
\[ x = \frac{2R}{4R} = \frac{2}{4} = 0.5 \]
Step 4: Final Answer:
The value of x is 0.5.