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GUJCET · Physics · Alternating Current
In LCR series ac circuit at, resonance, the value of power factor will be ______________ .
- A \(0\)
- B 1
- C -1
- D \(\infty\)
Answer & Solution
Correct Answer
(B) 1
Step-by-step Solution
Detailed explanation
(B) 1
Impedance \(Z=\sqrt{R^{2}+\left(X_{C}-X_{L}\right)^{2}}\)
At resonance \(X_{C}=X_{L}\)
\(\therefore \quad Z=R\)
Power factor \(\cos \phi=\frac{\mathrm{R}}{\mathrm{Z}}\)
\(
\begin{aligned}
& \cos \phi=\frac{\mathrm{R}}{\mathrm{R}} \\
& \cos \phi=1
\end{aligned}
\)
Impedance \(Z=\sqrt{R^{2}+\left(X_{C}-X_{L}\right)^{2}}\)
At resonance \(X_{C}=X_{L}\)
\(\therefore \quad Z=R\)
Power factor \(\cos \phi=\frac{\mathrm{R}}{\mathrm{Z}}\)
\(
\begin{aligned}
& \cos \phi=\frac{\mathrm{R}}{\mathrm{R}} \\
& \cos \phi=1
\end{aligned}
\)
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