Question

The phase difference between voltage and current in an LCR series circuit is :

• A. zero always
• B. $\pi /4$ always
• C. $\pi$
• D. between $-\pi /2$ and $\pi /2$

Answer 1

The correct option is D between $-\pi /2$ and $\pi /2$

The series RLC ciruit contains 3 elements, R, L and C connected in series connection.
Consider an AC source connected to the circuit with $\omega$ rad/s frequency.

Since we have L and C elements present in the circuit, they will offer some reactance depending on the freq.

Inductive reactance $=X_L=j\omega \times L$

Capacitive reactance $=X_C=\frac{1}{jw\times C}$

R remains unchanged as it is not a reactive element.

Now depending upon the operating frequency of the circuit there can be three cases of operation-

1. $X_L>X_C$ where the circuit will behave as an inductive circuit. Current flowing on the inductor will produce magnetic flux that have reverse direction with the source. When the current flowing at inductor is maximum, the voltage must be zero and vice versa. So the current is lagging $90$ degrees from the voltage
2. $X_C>X_L$ where the circuit will behave as a capacitive circuit. It has similar explanation with inductor but the current is leading $90$ degrees from the voltage
3. $X_L=X_C$ resonance condition.

So the phase of the source voltage and current can be anywhere from $-90$ to $+90$ degrees depending on element values and source frequency.