Question 258: AC fundamentals

Question

If the power factor changes from 0.5 to 0.25 because impedance changes from $Z_1$ to $Z_2$ then $\mathrm{Z}_1=\mathrm{xZ}_2$. The value of x is (Resistance remains constant)

Accepted Answer

Step 1: Recall Definitions
Power factor (p.f.) = cosÃ¢ÂÂ¯ÃÂ = $ R / Z $,
where $R$ is the resistance (constant here), and $Z$ is the magnitude of impedance.
So:
$ 	ext{p.f.} = \frac{R}{Z} $
Step 2: Write Relations
Initially:
$ \cos \varphi_1 = 	ext{p.f.}_1 = 0.5 = \frac{R}{Z_1} $
So:
$ Z_1 = \frac{R}{0.5} = 2R $
Then:
$ \cos \varphi_2 = 	ext{p.f.}_2 = 0.25 = \frac{R}{Z_2} $
So:
$ Z_2 = \frac{R}{0.25} = 4R $
Step 3: Relation Between $Z_1$ and $Z_2$
$ Z_1 = 2R, \quad Z_2 = 4R $
So:
$ Z_1 = \frac{1}{2} Z_2 $
Step 4: Final Answer
$ x = 0.5 $
Ã¢ÂÂ Correct option:
Option B (0.5)

Answer

0.1

Answer

0.5

Answer

0.7

Answer

0.4

AC fundamentals

If the power factor changes from 0.5 to 0.25 because impedance changes from Z_1 to Z_2 then \mathrm{Z}_1=\mathrm{xZ}_2. The value of x is (Resistance remains constant)

Choose the correct answer: