Question:
In an a.c. circuit, if the power factor changes from \(0.5\) to \(0.25\) then the increase in impedance is
In an a.c. circuit, if the power factor changes from \(0.5\) to \(0.25\) then the increase in impedance is
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Power factor is R over Z, so for fixed R the impedance is inversely proportional to the power factor.
Updated On: Nov 12, 2026
- twice
- half
- four times
- eight times
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept
The power factor is \(\cos\phi=\dfrac{R}{Z}\).
Step 2: Constant Resistance
If \(R\) stays the same, \(Z\propto\dfrac{1}{\cos\phi}\).
Step 3: Compare
\(\dfrac{Z_2}{Z_1}=\dfrac{\cos\phi_1}{\cos\phi_2}=\dfrac{0.5}{0.25}=2\).
Final Answer:
The impedance becomes twice its original value. \[ \boxed{\text{(A) }\text{twice}} \]
The power factor is \(\cos\phi=\dfrac{R}{Z}\).
Step 2: Constant Resistance
If \(R\) stays the same, \(Z\propto\dfrac{1}{\cos\phi}\).
Step 3: Compare
\(\dfrac{Z_2}{Z_1}=\dfrac{\cos\phi_1}{\cos\phi_2}=\dfrac{0.5}{0.25}=2\).
Final Answer:
The impedance becomes twice its original value. \[ \boxed{\text{(A) }\text{twice}} \]
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