Question 149: AC fundamentals

Question

A series L.R circuit connected with an ac source $$E=(25 \sin 1000 t) V$$ has a power factor of $$\frac{1}{\sqrt{2}}$$. If the source of emf is changed to $$\mathrm{E}=(20 \sin 2000 \mathrm{t}) \mathrm{V}$$, the new power factor of the circuit will be :

Accepted Answer

$$\begin{aligned}
& E=25 \sin (1000 t) \\
& \cos 	heta=\frac{1}{\sqrt{2}}
\end{aligned}$$
LR circuit
$$\begin{aligned}
& 	ext { Initially } \frac{R}{\omega_1 L}=\frac{1}{	an 	heta}=\frac{1}{	an 45^{\circ}}=1 \\
& X_L=\omega_1 L \\
& \omega_2=2 \omega_1, 	ext { given } \\
& 	an 	heta^{\prime}=\frac{\omega_2 L}{R}=\frac{2 \omega_1 L}{R} \\
& 	an 	heta^{\prime}=2 \\
& \cos 	heta^{\prime}=\frac{1}{\sqrt{5}}
\end{aligned}$$

Answer

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

Answer

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

Answer

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

Answer

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

AC fundamentals

A series L.R circuit connected with an ac source $E=(25 \sin 1000 t) V has a power factor of \frac{1}{\sqrt{2}}. If the source of emf is changed to \mathrm{E}=(20 \sin 2000 \mathrm{t}) \mathrm{V}$, the new power factor of the circuit will be :

Choose the correct answer: