4/18 Passive RC Circuit Natural Response & Passive RL Circuit Natural Response

We started with inductors with series and parallel.
It's the same as resistors.
The equivalent inductance of series-connected inductors is the sum of the individual inductances, and the equivalent inductance of parallel inductors is the reciprocal of the sum of the reciprocals of the individual inductances.

Here is the example we did in the class.

The equivalent inductance for this question is 15H.

Next, we talked about first order RC and RL circuits.

A source-free RC circuit occurs when its dc source is suddenly disconnected. The energy already stored in the capacitor is released to the resistors. A circuit response is the manner in which the circuit reacts to an excitation.

(From Day 16 1st Order Circuits.pdf)

There are two important relationships:

Both relations take 5 time constant to reach the final state or the steady state.

We did a example.

Passive RC Circuit Natural Response

Pre-lab

Estimation the time constant for the circuits of Figures 2(a) and 2(b).

For figure 2(a) the 5 time constant = 0.352s, and for figure 2(b) the 5 time constant = 0.0756s

The actual resistance for R1 = 0.977 ohms and R2 = 2.16k ohms.

This is the basic set up for this lab.

Figure 2(a)

We got almost the same value for the 5 time constant. (Forgot to take a picture for the initial time that started to drop)

Measured 5 time constant = 0.343s

Calculated 5 time constant = 0.352s

% error = 2.56%

Figure 2(b)

We got almost the same value for the 5 time constant. (Forgot to take a picture for the initial time that started to drop)

Measured 5 time constant = 0.08158s

Calculated 5 time constant = 0.0756s

% error = 7.91%

Passive RL Circuit Natural Response

Don't have time to do pre-lab

The picture below is the result for figure 2(a)

Summary

We learned how to deal with inductors with series or parallel, RC and RL circuits, and how to determine the time constant in a real world circuit.

Recently, if the class had the second lab at that day, the time would not be enough to finish the second lab. We spent to much time on the first lab. Limiting the time for the first lab would help to solve this problem.