Transient response of LCR circuits

schematics/RLC-circuit.svg

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

schematics/RLCtransient.svg pics/RLCtransient-screen.png

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, 1μF 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