D 12 - Capacitors and Inductors

We started the day with a discussion of why sometimes there is a spark when we plug stuff in, turns out to be because of capacitors and having mechanical engineers design electric circuits.

White Board work of why and how Capcitors charge. It is a function of A and d. Area and distance.

We then were asked to design our own version of a variable capacitor.

White Board work of our variable capacitors. Mine is on top with a triangle screw to close d, and Jon's is on the right with a squeezer on top to change d.

We then move onto solving for the energy in a capacitor, with P = VI and taking the integral. E = 1/2CV^2

White Board work for finding E. E = 1/2CV^2

We then drew the change of current over time. It is important to understand that the slope is what define the integral. Constants turn into linear and linear turns into parabolic.

White Board work of I versus t and we use the slope for the V versus t graph.

White Board work of V versus t took integrals of I.

We move onto an example of a DC capacitor circuit.

White Board work of the DC circuit, we turn capacitors to "open" and find Req.

More White Board work,  we found Va = 4 , Vb = 8V, then found E1 = 0.016 J and E2 = 0.128 J.

We then moved onto the lab of the day:
Capacitors Voltage-current Relations
Prelab:
We then sketch the "phase" shift the capacitors causes.

White Board work of the sketches of graphs for the capacitors. Sine wave. The shift is pi/2.

More White board work of the sketches with square waves and saw tooth wave. This also has the pi/2 shift. from I to V.

Picture of the capacitor circuit below.

Picture of our capacitor circuit.

More white board work with the equations used for Ir and Ic.

Picture of the signals before capacitor and after on the resistor.

Picture of the sine-wave going through the capacitor.

Picture of the freq 1khz period of 1ms and amp of 114 mV the M1 math value is 77uV,  C2 amp is 2 V freq of 1khz and period of 1ms.

Picture of the second sinewave input at 2 khz.

Picture of  C1 freq 2khz period 200us amplitude 218mV, and C2 amp 1.98V freq 2khz period 500us with M1 math value being 76uV.

Picture of the square wave being fed into capacitor.

Picutre of square wave, C1 amp 18 V freq 100 hz period 10ms, C2 amp 2.7 V freq 100 Hz period 9.99 ms M1 math value of 75 uV.

More sketch for the prelab for the sine wave, triangle wave and square wave expected outputs.

White board for prelab expectations of the output across the resistor. Our expected results matched the output graphs from the oscilloscopes taken for each one.

We then move onto how capacitors work in series and parallel. We did an example with capacitors below.

White Board work of capacitors in series and parallel, series you C1C2/(C1+C2), parallel add C1+C2.

More White Board work, with talked about how finding C and finding L.

Lastly we talked about how Inductor are like everything like a capacitor but different. Like for adding in series and parallel they the opposite. After 10 minuets of inductor knowledge can be summed on the white board picture below.

White Board knowledge of summarizing Capacitors and Inductors, same thing but different.

In summary we learned how capacitors charge up and how find the energy stored in a capacitor by using E = 1/2CV^2. Learned that capacitors in a DC setting act like an open. Did a lab on capacitors and found the phase shift of pi/2. Talked about inductors how they relate to capacitors. We found our expected graphs matched the output on the oscilloscopes. We then finished the class with an example of capacitors in series and parallel. In series C1C2/(C1+C2) and parallel C1+C2. Lastly we said inductors behave opposite of capacitors and made a white board with all the difference on it.