Question 57: AC fundamentals

Question

For the series LCR circuit connected with $220 \mathrm{~V}, 50 \mathrm{~Hz}$ a.c source as shown in the figure, the power factor is $\frac{\alpha}{10}$. The value of $\alpha$ is $\_\_\_\_$ .

Accepted Answer

The power factor ( $\cos \phi$ ) of an AC circuit is defined as the ratio of the true resistance (R) to the total impedance (Z) of the circuit.
Power Factor $=\cos \phi=\frac{\mathrm{R}}{\mathrm{z}}$
In a series $L C R$ circuit, the inductive reactance $\left(X_L\right)$ and capacitive reactance $\left(X_C\right)$ oppose each other. The net reactance is the difference between them.
$$ \mathrm{X}=\left|\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right| $$
Substituting the given values :
$$ \mathrm{X}=|70-150| \Omega=80 \Omega $$
The total impedance of the circuit is,
$$ Z=\sqrt{R^2+X^2} $$
$$ \mathrm{Z}=\sqrt{(60)^2+(80)^2}=\sqrt{10000}=10 \Omega $$
So, the power factor is $\cos \phi=\frac{\mathrm{R}}{\mathrm{Z}}=\frac{60}{100}=\frac{6}{10}$
$$ \Rightarrow \frac{\mathrm{a}}{10}=\frac{6}{10} $$
$$ \Rightarrow a=6 $$
Therefore, the value of a is 6 . Hence, the correct option is (C).

Answer

4

Answer

8

Answer

6

Answer

10

AC fundamentals

For the series LCR circuit connected with 220 \mathrm{~V}, 50 \mathrm{~Hz} a.c source as shown in the figure, the power factor is \frac{\alpha}{10}. The value of \alpha is \_\_\_\_ .

Choose the correct answer: