Question

In an $AC$ series circuit given that, $R=10\Omega$, $X_L=20\Omega$ and $X_C=10\Omega$. Then choose the correct options

• A. Voltage function will lead the current function.
• B. Total impedance of the circuit is $10\sqrt{2}\Omega$
• C. Phase angle between voltage function and current function is ${45}^o$
• D. Power factor of circuit is $\frac{1}{\sqrt{2}}$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A Voltage function will lead the current function.
B Power factor of circuit is $\frac{1}{\sqrt{2}}$
C Total impedance of the circuit is $10\sqrt{2}\Omega$
D Phase angle between voltage function and current function is ${45}^o$

(a) Since $X_L>X_C)$, hence voltage function will lead the current function.
(b) Impedance of the circuit $Z=\sqrt{R^2+(X_L-X_C{)}^2}$
$Z=\sqrt{(10{)}^2+(20-10{)}^2}$
$Z=10\sqrt{2}\Omega$
(c) $\cos \varphi =\frac{R}{Z}=\frac{10}{10\sqrt{2}}=\frac{1}{\sqrt{2}}$
Hence, phase angle $\varphi ={45}^o$
(d) Power factor $\cos \varphi =\frac{R}{Z}=\frac{1}{\sqrt{2}}$