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: Power Factor Formula
$\cos \phi = \frac{R}{Z}$. Since $R$ is constant, $\cos \phi \propto \frac{1}{Z}$.
Step 2: Set up Ratio
$\frac{\cos \phi_1}{\cos \phi_2} = \frac{Z_2}{Z_1}$
Step 3: Calculation
$\frac{0.5}{0.25} = \frac{Z_2}{Z_1} \Rightarrow 2 = \frac{Z_2}{Z_1} \Rightarrow Z_1 = \frac{1}{2} Z_2$
Step 4: Finding x
$Z_1 = 0.5 Z_2$. Thus, $x = 0.5$.
Final Answer:(B)