05-12-2016

Lecture:The Impedance of inductor and capacitor

I. Introduction:

For today lecture, we will continue our studying the with impedance of capacitor and inductor in AC circuit

The impedance have two parts, the real part is called pure resistance, whereas the imaginary is called the reactive part.

Impedance can be known as the resistor in AC circuit, using that knowledge, omh law still holds for voltage and current, with one more imaginary term

Here we convert everything back to frequency domain to do the calculation, after we finished we converted everything back to time domain

II. Impedance Lab:
The purpose of this lab is to check the understanding of impedance. The frequency will affect the ratio of Vo/Vin in this lab. 
For this lab, the frequencies we used are 1kHZ,5kHZ,10kHZ

Here is our data collection, only the impedance of capacitor and inductor affected by the frequency The gain of overall circuit will not be affected by the frequency.

Graph of 1kHz

Here is our setup

I=V/Z=0.036cis-34.4,
Vout/Vin=X/(R+jXL)=0.56cis55.6

Here there is some lagging between the inductor and the capacitor

Here is our derivation to find out the Zequi in the circuit

since the angle is 45, which tells us the gain is 45 degree. The phase between Vo and Vin is 45

III. Conclusion:
For this lab, we learned how to apply phasor transformation to solve for many problems within frequency domain. With phasor converts everything to the impedance, we now can use the techniques we had learned before, namely, nodal analysis, mesh current and so on. The only thing that difference is that the frequency could affect the impedance of capacitor and the inductor