Day fourteen - RC and RL 4/18/2017

Hey guys, today we talked about two first-order circuits, RC and RL circuits.

There are two ways of exciting the RC and RL circuits. The first method is by the source-free circuit and the second method is by independent sources.

The source-free circuit is triggered when the dc source is suddenly disconnected.
When applying source-free circuit to the RC and RL circuit, a response called natural response will occur, and this response is characterized by the initial energy stored and the physical characteristics of the circuit without being affected by the external voltage or current source.

It turns out that the voltage in both RC and RL circuits triggered by the source-free circuit will behave like exponential decay equations.

LAB - Passive RC Circuit Natural Response


Pre-Lab

Here is the schematic of the circuit I implemented.

Using the given values of resistors, we calculated that the initial voltage of the capacitor is       

v = 5/(1k+2.2k)*(2.2k) = 3.4375volt and the initial time constant is RC = (2.2k)(22*10^-6) = 0.484s

Result

Actual Resistance values are 0.977k for 1k and 2.16k for 2.2k resistors.

However, we are not able to measure the value of the capacitor.

This is our result from part 2(a), and we measured with a 3.454volt at the peak. If we compare this value to our calculation using the actual values, the difference is only 3.454 - 3.442 = 0.011volt which is like smaller than 1% of percent error.
Our measured time constant is measured by assuming the voltage will decrease 99% of the original voltage, so we measured the time of voltage dropping from 3.454V to 33.97mV, and takes this time as 5RC, then we get 27.58ms.
Comparing to our calculated value of 5RC = 0.2376s, the percent error is 16%, without knowing the actual value of the capacitor, the percent error might still verify the voltage difference of natural response.

This is our result from 2(b). Our measured values of initial voltage = 3.494volt, and our calculated values using actual values is v = 3.442volt, by comparing them, we get 1.5% error. This error is acceptable because every circuit component is not perfect, there can be some voltage leak on each component. Similar to 2(a), we get the time of 5RC and compare it with calculated value.
Calculated 5RC = 5(0.014799) = 0.073995.
Approximate measured 5RC = 81.58ms.
Comparing both values, we have 10% error, and this should be considered as successful verification
because the measured value is an approximation, and this approximation can apply to all experiment today we have done.

LAB - Passive RL Circuit Natural Response

Pre-Lab

The initial current is I = 5/1k = 5*10^-3A because the inductor is simply a short-circuit to a dc. The time constant L/R = (0.001H)(2.2k) = 4.5454*10^-7s

Actual resistance values of resistors are 0.977k (R1) and 2.16k (R2) ohms.

Result

This is the result of part 2(a). 

This should be the result of part 2(b); however, we are unable to collect the actual data of this experiment because my computer shut down after I got the data. This lab will be redo.

Summary:
From today lecture and experiment, I learned that the natural response of both RC and RL circuits will undergo exponential decay, and when the time is 5(time constant), the value will be 0.01% of the original value, so we consider time constant = 5 as all energy is used. One important point to remind ourselves is that on a dc circuit, the capacitor is a open circuit and the inductor is a short circuit.