lab report

Name: Huy Dang

Class: ECE 109L-06

Group #:4

Experiment 7

Measure an Unknown capacitor

1. Executive Summary

This experiment will introduce the concept of capacitor. A capacitor is a circuit element that can store charges. RC (resistor-capacitor) circuit are heavily dependent on the time constant. Theoretically, after one time constant, the voltage in capacitor will reach Vs(1-e-1) which is 63% of Vs. It’s a common practice to assume that the capacitor will reach steady state (fully charged) at 5 time constant.

2. Objective

The objective of this experiment is to find out the value of an unknown capacitor. We will do this by connecting a circuit involving a capacitor, a resistor, a voltage source and an oscilloscope.

3. Graph

Figure 1: Overview of the charges in the capacitor.

Figure 2: Zoom in version of figure 1 with Δx label.

4. Data

Resistor Value	10kΩ
Frequency of Function Generator	230 Hz
Vs	10V
Voltage at one time constant	1.321 V
One Time Constant	184 µs
Cmeasured	.0184µF
Cactual	.022µF
Relative Error between Cmeasure and Cactual	16.4%

5. Analysis

Using the oscilloscope, we were able to figure out the value of time constant. This value is represented as Δx. This is the time it took for the charge to reach 1.321V or 63% of the total charge (note that the graph input signal start at -5 not 0, therefore at 1.321V it is actually 6.321V). After figuring out the time constant, we can use the simple equation ᴛ = RC. We achieved the value of .0184µF for our capacitor, a difference of 16.4% from the actual value of .022µF. This error is due to the fact that our method for determining Δx doesn’t have a high accuracy to it. We simply estimate the value using the cursor on the oscilloscope. Since all of the cursor values are quantized, we can not get the most accurate result from our experiment. Also, the capacitor we received were of a bad batch, there’s a high chance that the actual value of the capacitor is not .022µF.

6. Conclusion

For the lab, the frequency is set at 230 Hz due to the fact that we need to see approximately 10 times constant in a half cycle of the square wave. When observing figure 1, we can see that the yellow square wave fits almost perfectly with the green charges from the capacitor. Frequency different from 230 Hz will cause a distortion, causing us to ineffectively able to measure the necessary value.

The frequency of the waveform can be measured by using the length of the x axis display and the amount of period represented. We can used the amount of period, divided by the time display of the x-axis to achieve the frequency.

Although we have a high percent error associated with our experiment, this is mostly due to faulty equipment and low accuracy measurement method. However, we were able to get a value relatively close to the actual value. Therefore, we can conclude that we have achieved the objective of finding an unknown capacitor using the above method.