Passive RC Circuit Natural Response & Passive RL Circuit Natural Response

Today we went over the charging and discharging process of capacitors and inductors. Theoretically speaking, it takes infinite time for a capacitor or inductor to charge or discharge. In engineering world, we consider a capacitor or inductor as completely discharged after 5 time constants. After five time constants, the remaining energy is less than 1%. In other words, we can measure the time it takes to almost drop to 0 energy and divide it by 5 to get the time constant. We apply this method in the following two labs

Passive RC Circuit Natural Response

This lab examines the natural response of an RC circuit. we use manual switch and square wave voltage source to create the natural response.

Here is a schematic of the circuit with theoretical values

We observed the voltage response on the oscilloscope window

We compared the values from the oscilloscope and the theoretical values.

	Experimental	Theoretical	Percent Error
Charging Time (ms)	79.9	76	5.13%
Discharging Time (ms)	242.6	242	0.25%

Then we applied a square wave instead of manually switching it.

	Experimental	Theoretical	Percent Error
Charging Time (ms)	74.03	76	2.59%
Discharging Time (ms)	273.7	242	13.10%

Passive RL Circuit Natural Response

This lab uses an inductor instead of a capacitor. The other parts of the circuit stay the same. 

Here is a schematic of the circuit

Here is the circuit setup

We adjust the frequency to get the time constant.

Summary: The natural response of capacitors and inductors indicates that there is a maximum switching frequency. Since a capacitor or inductor in a circuit takes a certain time to drop its voltage or current to a very small amount, switching to fast would cause the a capacitor or inductor to start discharging before it is fully charged or start charging before it is fully discharged. We normally consider a capacitor or inductor is fully charged or discharged after 5 time constants. The maximum switching frequency should be less than its reciprocal.