Question 341: AC fundamentals

Question

The power factor of an R-L circuit is $\frac{1}{\sqrt{2}}$. If the frequency of $\mathrm{AC}$ is doubled the power factor will now be

Accepted Answer

The power factor of an R-L circuit is given as,
$\begin{aligned}
& \cos \phi=\frac{\mathrm{R}}{\sqrt{\mathrm{R}^2+\mathrm{X}_{\mathrm{L}}^2}} \
& 	herefore \quad\frac{R}{\sqrt{R^2+X_L^2}}=\frac{1}{\sqrt{2}} \
& 	herefore \quad\frac{1}{\sqrt{1+\left(\frac{X_L}{R}ight)^2}}=\frac{1}{\sqrt{2}} \
& 	herefore \quad\frac{1}{\sqrt{1+\left(\frac{\omega L}{R}ight)^2}}=\frac{1}{\sqrt{2}} \
& 	herefore \quad\left(\frac{\omega L}{R}ight)^2+1=2 \
& 	herefore \quad\frac{\omega L}{R}=1 \
\end{aligned}$
So, when the AC frequency is doubled,
$\begin{aligned}
& \quad\frac{\omega L}{R}=2 \
& 	herefore \quad\cos \phi=\frac{1}{\sqrt{1+\left(\frac{\omega L}{R}ight)^2}}=\frac{1}{\sqrt{1+(2)^2}} \
& 	herefore \quad\cos \phi=\frac{1}{\sqrt{5}}
\end{aligned}$

Answer

$\frac{1}{\sqrt{3}}$

Answer

$\frac{1}{\sqrt{5}}$

Answer

$\frac{1}{\sqrt{7}}$

Answer

$\frac{1}{\sqrt{11}}$

AC fundamentals

The power factor of an R-L circuit is \frac{1}{\sqrt{2}}. If the frequency of \mathrm{AC} is doubled the power factor will now be

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