# Transient response of LCR circuits

Closing the switch in the cicuit shown above will change the voltage across the capacitor. Depending on the relative values of L, C and R, the voltage may show oscillations or it may change in an exponential manner.

# Objective

Apply a step voltage to an LCR circuit. Capture and analyse the resulting voltage across the capacitor.

# Procedure

- Use the 3000 turn coil and 0.1 μ F capacitor
- Click on 5->0V STEP. Adjust x-axis and repeat if required.
- FIT the graph to find the resonant frequency & Damping factor.
- Repeat with increased capacitance and resistance values.

The values chosen are for an underdamped response. The coil has in inductance more than 100mH and a resistance of around 500Ω. To increase damping, you may add a series resistor, or use a larger value capacitor.

# Discussion

Explore the oscillatory nature of L and C in series. Resonant frequency of series LC circuit is given by f0= 1 ⁄ (2π√(LC)). The damping factor is R⁄ (2√(LC)), and it is equal to 1 for critical damping. Depending upon the value of C/L and R, the response could be under-damped, critically-damped or over-damped.

We have used the 3000 turn coil and a 0, 1 μ F capacitor. The voltage across the capacitor after a 5 to 0V step is shown in figure. The measured resonant frequency tallies with f= 1 ⁄ (2π√(LC)), within the component tolerance values.

https://en.wikipedia.org/wiki/RLC_circuit