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