Lab:Capacitor/Inductor Voltage-current Relations(April 13, 2017)

Date: April 13, 2017

Capacitor; Capacitor Voltage-current Relations; Inductors; Inductor Voltage-current Relations

Activity 1: Capacitors in a Circuit

            In this activity, we use our understanding of how capacitors work in a DC-circuit to obtain the amount of energy at each capacitor.

            In the picture above, the circuit is in DC-circuit; therefore, we replace all the capacitors with open circuits. Because of this, we can now find the current, I, because the resistors are all in series. Then, we find the voltages parallel to the capacitor because they will be the same. Now that we have the voltage at each capacitor, we use the energy equation for capacitors to solve for W1 and W2.

Lab 1: Capacitor Voltage-current Relations

Pre-lab:

In the above picture, we did the pre-lab where we sketched out the capacitor voltage-current relation. The top graph was for a sinusoidal wave and the bottom graph was for a triangular wave.

We were given that the resistor was 100ohms and the capacitor was 1microF. We also put down the voltage we were applying and the frequency.

For the picture above, the frequency was 1k-Hz and was a sinusoidal wave input.

The picture above was for 2k-Hz and was a sinusoidal wave input.

This picture was for 100Hz and was for a triangular wave input.

When we compare these to the pre-lab sketches we did, we confirm that our prediction was correct.

Activity 2: Capacitor Equivalence

This activity serves to remind us that the equivalent capacitor can be determined just like the equivalent resistor.

The above picture shows step by step how each equivalent capacitor is calculated. In series, they add together; in parallel, they follow Req=(R1+R2)/(R1*R2).

Activity 3: Inductors

This activity serves as practice for using the inductors to find current.

This is the picture of the question.

This is the step by step of solving for the current when an inductor is in the circuit. First, we note that the voltage across an inductor is a time dependent event. Then we write down the relationship between voltage, inductors, and current. We solve for di then integrate to get current. We plug in all the values to get the current at the specific time, i(t). Then we realized that they gave us the initial current; therefore, we add them together to get the final current.

Lab 2: Inductor Voltage-current Relation

In this lab, our aim was to analyze the relation between the voltage difference across an inductor and the current passing through it.

In the picture above, we applied a sinusoidal input voltage at 1k-Hz, amplitude of 2V, and was offset to 0V.

In the picture above, we applied a sinusoidal input voltage at 2k-Hz, amplitude 0f 2V, and was offset to 0V.

In Conclusion:

            Today, we learned about capacitor, inductors, and their relation of the voltage and current running through them. In the first lab, we see that regardless of the type of voltage wave we insert to the capacitor, the current wave will be the derivative of that voltage wave. The second lab showed us that changing the frequency results in a change in amplitude for the current.