Question 284: AC fundamentals

Question

In an electrical circuit ' $R$ ', ' $L$ ', ' $C$ ' and an a.c. voltage source are all connected in series. When ' L ' is removed from the circuit, the phase difference between the voltage and the current in the circuit is $\frac{\pi}{3}$. If instead ' $C$ ' is removed from the circuit, the phase difference is again $\frac{\pi}{3}$. The power factor of the circuit is $\left(	an \frac{\pi}{3}=\sqrt{3}ight)$

Accepted Answer

When L is removed,
$$ \begin{aligned} & \frac{X_C}{R}=	an \frac{\pi}{3} \ 	herefore & X_C=R 	an \frac{\pi}{3} \end{aligned} $$
When C is removed,
$$ \begin{aligned} & \frac{X_L}{R}=	an \frac{\pi}{3} \ & X_L=R 	an \frac{\pi}{3} \ 	herefore \quad & Z=\sqrt{R^2+\left(X_L-X_Cight)^2}=R \ 	herefore \quad & \cos \phi=\frac{R}{Z}=1 \end{aligned} $$

Answer

$\frac{\sqrt{3}}{2}$

Answer

$\frac{1}{2}$

Answer

$\frac{1}{\sqrt{2}}$

Answer

1

AC fundamentals

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