14-Apr-2015: Capacitor Voltage-Current Relations

PURPOSE

The purpose of this experiment was to get us more familiar with the relationship between the voltage and the current across a capacitor.

PROCEDURES

Figure 1

We began this experiment by constructing the set-up shown above in Figure 1. It was a relatively simple circuit as it consisted of a single capacitor, a resistor and a voltage source. We varied the voltage source in terms of shape, frequency, and amplitude and observed how the voltage across the resistor responded to these variations. In addition, we set up a math channel to find the current across the capacitor, which was the same as the current across the resistor since the capacitor and the resistor were in series. Therefore, we concluded that the current across the capacitor was simply the resistor voltage divided by the resistance value of the resistor.

First, we applied a sinusoidal input voltage with an amplitude of 2 V, oscillating at a frequency of 1 kHz. The resulting voltage across the resistor and the current across the capacitor was displayed on an oscilloscope along with the input voltage, as shown in Figure 2 (click to enlarge). The amplitude, frequency, and period of the output voltage were also displayed on the oscilloscope.

Next, we applied another sinusoidal voltage to the circuit. We kept the amplitude constant and just increased the frequency to 2 kHz. The resulting output graphs are illustrated in Figure 3 (click to enlarge). As it can be seen from the image, the amplitude of the resistor voltage actually decreased as a result of the higher input frequency.

Finally, we applied a triangular voltage with a frequency of 100 Hz and an amplitude of 4 V. The graph of the output voltage was close to rectangular in shape. The curved parts of the graph can be attributed to the delay of the response of the resistor voltage to the abrupt changes of the input voltage.