Q. In a series L – C – R circuit, resistance $R = 10\ \Omega$ and the impedance $Z = 10\ \Omega$. The phase difference between the current and the voltage is
A) $0{^\circ}$
B) $30{^\circ}$
C) $45{^\circ}$
D) $60{^\circ}$
Explanation
(a) Impedance,
$\ \ \ \ \ \ \ \ \ Z = \sqrt{R^{2} + \left( X_{L} - X_{C} \right)^{2}\ }$
$\therefore\ \ \ \ \ 10 = \sqrt{(10^{2} + \left( X_{L} - X_{C} \right)^{2}}$
$\Rightarrow \ \ 100 = 100 + \left( X_{L} - X_{C} \right)^{2}$
$\Rightarrow \ \ \ \ \ \ \ X_{L} - X_{C} = 0$ …(i)
Let $\phi$ is the phase difference between current and voltage
$\tan{\phi = \frac{X_{L} - X_{C}}{R}}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \tan{\phi = \frac{0}{R}}\ \ \ $
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \phi = 0$ [From Eq.(i)]
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.