Capacitor Lab

In this lab assignment we dealt with RC circuits in both the charge and discharge case, or in other words, the source and source-free cases, where the time constant tau=RchargeC or tau=RdischargeC control the rate at which energy is transferred. This lab allows to reinforce the concepts learned in the lecture. 

After reading through all of the theory, our first task was to calculate expressions for the Thevenin voltage and resistance for the charge case as well as for the discharge case:

In our experiment, we were to use a 9 V power supply along with transient interval of 20 s with an energy storage of 2.5 mJ as well as discharge transient interval of 2 s with the same energy. Step 2 required us to (a) compute the required capacitance C, (b) estimating the value of the charging resistance Rcharge, and (c) to calculate the peak current Imax and the peak power Pmax for the charging case. Here are the results that we obtained:

Likewise, in the discharging case we were asked to compute (a) the estimated value of the discharge resistance Rdischarge, (b) the peak discharge current Imax and peak power. Here are the results that we obtained:

Step 4 required us to build the circuit.  Like what I mentioned earlier, we were required to set the voltage supply to 9V using a DMM. Then we were to build the circuit using a jack on the breadboard as the common point in the circuit. We were also given some pointers that the leakage resistance is part of the variable capacitor box and that the red and black terminals should be connected to the scope. Step 5 required us to configure our test equipment. We were originally supposed to use an oscilloscope, but our instructor required us to use the LabPro software as a substitute. The photo below shows the setup for Steps 4 and 5.

Now for Step 6, we were to perform the actual experiment. First we energized the power supply to 9 V. Then we were to determine Rcharge by connecting the cable of the red terminal of the capacitor box to the variable resistor box. Using the data from LoggerPro, we noticed that the final voltage from the effect of Rleak came out to be Vfinal= 5.93, noting that the theoretical value of 9V could not be obtained because of saturation reasons.  The LoggerPro data and it's corresponding graph are lsited below. We did notice that it indeed took about 20 s to charge. 

                 

Next, we were required to solve for Rleak for the given equation in the photo below. 

Now we were to perform the discharging case. Please refer to the to the LoggerPro photo up above for the graphical details. After allowing the RC circuit to charge for five time constants (1.e. for 20 seconds) we quickly connected the capacitor cable to the Rdischarge resistor. As you can see the discharge transients took about 2 seconds. 

Now for the analysis questions we were required to compute the Thevenin equivalents for both the charging and discharging cases.  

Next, we were required to required to the value of Rcharge at one time constant. From the LoggerPro waveform, we estimated the time constant to be about 4 s. This allowed us to compute Rcharge, which is shown in the photo below:

Now we were required to answer a question for Part 8. Given an energy value of 160MJ and a voltage of 15kV, were were asked to find the required equivalent capacitance. Here is what we obtained:

Finally, we were asked to compute the individual capacitance of the series-parallel capacitor network shown below:

For each branch, the series capacitors are combined to given an equivalent capacitance of C/2 for each branch. Then since each of the four branches are in parallel with each other, then combined to give Ctotal = 4(C/2) = 2C = 2(1.42 F) = 2.84 V.

This was an interesting lab that really helped us reinforce the concepts of RC transients and helped relate the theory to a real-life situation. We considered our lab to be a success because our transients occurred approximately at the computed theoretical value of five time constants. Hopefully this success will continue into the remaining lab assignments for this semester.