Lab Report Day Thirteen - Capacitor Voltage-Current Relations

In this assignment, we measure the relationship between the voltage difference across a capacitor and the current passing through it. We apply several types of time-varying signals to a series combination of a 100 ohm resistor and a 1u (micro) capacitor. The voltage difference across the resistor, in conjunction with Ohm’s law, will provide an estimate of the current through the capacitor. This current can be related to the voltage difference across the capacitor.

We apply three waves with different frequency across the circuit using Analog Discovery. We apply two sinusoidal waves with magnitudes of 2 V and frequencies of 1k Hz and 2k Hz, and one triangular wave with magnitude 4V and a frequency of 100 Hz.We are asked to predict what would happen to the current.

Here is our predicted graph.

Here are our measured R and C. Our theoretical values are 100 ohm and 1 u F, and our experiment value is 100.1 ohm and 1.096 u F, which are very close. 

This is the set up of our circuit.

The first time varying signal sent into the circuit was a sine function with an amplitude of 2V and a frequency of 1kHz.

The second time varying signal sent into the circuit was another since function but the time with a frequency of 2kHz.

The last time varying signal sent into the circuit was a triangular function with an amplitude of 4V and frequency of 100Hz.

Analysis: 

As what we see from the screenshot,  our predictions are almost. We use Ohm's law, I=V/R to get the measurement if current in mA.  We can see that the current through the capacitor has a 90 degree phase shift (Max or min to the middle point of V).

Summary:

Today we learn about capacitors and inductors. When calculating capacitor's capacitance, they add together when they are in parallel, and add inversely while in series. We can draw non-ideal capacitor  a resistor in parallel with it. Inductors are mostly coils of wire. When calculating the inductance of inductors, they just act like resistors. We can draw non-ideal inductor with a resistor in series. In DC, capacitor acts as open circuit, and inductor acts as short circuit.