Question

In series LCR circuit, the phase difference between the applied voltage and current is
A. Positive when $X_L>X_C$
B. Positive when $X_C>X_L$
C. 90°
D. 0°

Answer 1

Hint: This problem can be solved by using the formula for phase difference between the applied voltage and current in series LCR circuit. This formula gives the relation between phase angle, impedance of conductor and impedance of conductor. Substitute the conditions given in the formula for phase difference. Substituting these conditions will give the phase difference between applied voltage and current in a series LCR circuit.

Formula used:
$\tan \varphi ={\displaystyle \frac{X_L–X_C}{R}}$

Complete step-by-step answer:
In a series LCR circuit, the phase angle is given by,
$\tan \varphi ={\displaystyle \frac{X_L–X_C}{R}}$
Where, $\varphi$ is the phase difference between the applied voltage
             $X_L$ is the impedance of inductor
             $X_C$ is the impedance of conductor
$\Rightarrow \varphi ={\tan }^{-1}{\displaystyle \frac{X_L–X_C}{R}}$
When $X_L>X_C$, $\varphi$ is positive.
When $X_C>X_L$, $\varphi$ is negative.
When $X_C=X_L$, $\varphi$ is 0.
Hence, in series LCR circuit, the phase difference between applied voltage and current is Positive when $X_L>X_C$ and zero when $X_C=X_L$.
So, the correct answer is options are A and D i.e. Positive when $X_L>X_C$ and 0° respectively.

So, the correct answers are “Option A and D”.

Note: To solve these types of problems, students should remember the formula of phase difference between current and applied voltage in a series LCR circuit. The phase difference between the applied voltage and current can be negative as well as positive. Positive phase difference means that the voltage is leading the current by the phase angle. When the phase difference is negative, the current leads the voltage by the phase angle.