14 Jul 2026

Response Curve of a Parallel LCR Circuit

practical ug-ii electronics parallel-lcr anti-resonance

Aim

To study the response curve of a parallel LCR circuit and determine the anti-resonant frequency and quality factor.

Apparatus

Inductor, capacitor, resistor, audio frequency oscillator, AC milliammeter, voltmeter, connecting wires, and circuit board.

Circuit Diagram

Parallel LCR circuit used for anti-resonance study.

Theory

In a parallel LCR circuit, anti-resonance occurs when the inductive and capacitive branch currents cancel each other. At this frequency the supply current is minimum and the impedance is maximum.

The anti-resonant frequency is approximately

\[f_0=\frac{1}{2\pi\sqrt{LC}}.\]

For a practical parallel resonant circuit, the quality factor gives the sharpness of anti-resonance.

Observations

Frequency (Hz)	Supply current (mA)
300	42
400	36
500	28
600	19
700	11
800	6
900	10
1000	17
1100	25
1200	32
1300	38

Graph

Parallel LCR response curve showing minimum supply current at anti-resonance.

From the graph,

\[f_0=800\text{ Hz}.\]

For trial values $L=0.050\text{ H}$ and $C=0.80\,\mu\text{F}$,

\[f_0=\frac{1}{2\pi\sqrt{LC}}=795.8\text{ Hz}.\]

Result

The anti-resonant frequency of the parallel LCR circuit is approximately

\[\boxed{f_0=800\text{ Hz}}.\]

Precautions

1. Keep the input voltage constant throughout the experiment.
2. Take more readings near the minimum-current point.
3. Avoid loose contacts in the parallel branches.
4. Use components of proper voltage and current ratings.
5. Keep the inductor away from magnetic materials.

Viva Questions

1. What is anti-resonance?
   It is the condition in a parallel LCR circuit where the supply current is minimum.

2. What happens to impedance at anti-resonance?
   The impedance becomes maximum.

3. Why is the supply current minimum?
   The inductive and capacitive branch currents cancel each other partly.

4. How is parallel resonance different from series resonance?
   In series resonance current is maximum, whereas in parallel resonance supply current is minimum.

5. What is quality factor?
   It measures the sharpness of the resonance or anti-resonance curve.

Maxima Code

The calculation can be checked with this file: parallel-lcr-calculation.mac.