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
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 500 .
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 . The damping
factor is
, 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 capacitor. The voltage
across the capacitor after a 5 to 0V step is shown in figure. The
measured resonant frequency tallies with
,
within the component tolerance values.