D13 - 1st Order Circuits

We started the class with what questions would be on the day of celebrations.

The Six question type to be on the day of celebrations.

We then move onto finishing our talk of inductors. Inductors in parallel L1*L2/(L1+L2), in series L1+L2. We did a example below.

White Board work of inductors in series and parallel, in series they just add, while in parallel they L1L2/(L1+l2).

We then further discussed the difference in capacitors and inductors.

White Board knowledge, inductor for i integrate, while i for capacitors take derivative.

We then did some first order derivations to show that inductors behave first order like.

White board work for finding Vo using first order.

More White Boar work for finding Tao of the capacitor. We took Tao = RC and found after 5 Tao there is nothing left in capacitor.

We continued to explore the current by using V = IR. Power = I^2R

White Board work using Tao of a capacitor, note that 2*tao and everything else is the same for power.

We then move onto  source free examples.

White board work for V. We used source free and then Tao for RC and got Vc of cap and Ic of cap.

More white board work and we figured the time constants of Tao range form nanoseconds to hundred seconds.

We then move onto the first lab of the day:
Passive RC circuit Natural Response.
Prelab:
R1 = 971 ohms, R2 = 2.16 k ohms, C = 22uF. After 5 tao's Vc should be near zero. Tao is 15.

Picture of the Passive Capacitor circuit.

Picture of capacitor discharging by hand feeding in and out, after 5 Tao's its close to zero. 1 Tao = 15ms.

Another picture showing Tao and voltage at those points, starts at 3.4 V, after 15ms (1 Tao) drops to 2.67 V, and after 5 Tao (75ms) V drops to 0.891 V

Another picture of the capacitor discharging with hand feeding and pulling out.

Picture of waveform feeding the capacitor. Note the drops look the same as the disconnect above.

Another picture showing the amplitude 1.75 V and maximum of 3.45 V.

Picture below with trigger of one of the humps shown above.

Close up picture of one of the humps, same as the disconnect discharge.

Picture of the hump data, same amp and max as before, since it the same trigger data.

Picture of more data, however note the Tao is the same of 15ms and after 5 Taos (75ms) V is near zero. Just like the previous example.

We then move onto a source free inductor example with inductors with a switch component added to it.

White Board work, inductors act like a short in DC settings. Tao = L/R.

We then move onto the second lab of the day:
Passive RL circuit Natural Respond
Prelab:
Same resistance values of before, r1 = 971 ohms, r2 = 2.16 k ohms however L = 1mH. Tao is 1.7us.

Picture of the inductor circuit.

Picture of the fast disconnect and reconnect on the inductor.

Picture of the data from the quick disconnect reconnect. Amp = 1.2V max = 2.4 V.

Second part we assigned square wave to the inductor.

Picture of square wave feeding into inductor. Amp at 2.5 V offset at 2.5 V we changed to frequency to making feeble to see with diligent.

Another picture of data from the squarewave max and amp the same.

White board work showing how we got Tao to equal 1.7us. We noted we need to change the frequency higher then the lab requested since our time constant was so small, we ended up using 1k hz.

In summary we talked about inductors and how they behave in series and parallel. And then did first order problems with capacitors and inductors. We then did two labs showing how reliable our Tao constants calculated are close to in actual circuits. The first being in a capacitors which match our time constant perfectly, 15 ms and after 5 Taos zero Volts which matched the 75ms. For the inductor lab we found tao to be 1.7us which very small so we had the option to change R or change frequency in the circuit to get reliable data out of the oscilloscopes, we chose the frequency change to 1k hz. We found our Tao matched the one observed in the oscilloscope, however the picture can't be found :(
Lastly we talked about source free problems on which capacitors are open, and inductors are shorts.