week 11 day 2

Lecture

Solving addition of cos and sin using a graphical representation:

Leading and lagging between 2 sinusoidal functions:

 Converting complex number to its polar form:

 Using complex identities to solve complex number operation:

 Changing current from time-dependent form to phasor form :

 Voltage conversion from exponent form to it's phasor form, the bottom part of the board, changing the current from rectangular form to it's time dependent form :

Adding two voltage with different phase angles:

 Solving current by using factor and Impedance:

Passive RL Circuit Response Lab

Pre-Lab : 

Calculating theoretical phase shift  between input  current and voltage with 𝝎= cutoff frequency,  𝝎=1/10 cutoff frequency, and 𝝎=10 cutoff frequency

View of our circuit :

 Input voltage versus input current at 𝝎= cutoff frequency

Input voltage versus input current at 𝝎= 1/10 cutoff frequency

Input voltage versus input current at 𝝎= 10 cutoff frequency

we measure the distance between each peak and dividing over the period of the sinusoidal function to measure the phase shift between the current and voltage. Below are the calculated theoretical value and measured the experimental value of our trials:

Summary 

In AC circuit, It's easier to analyze circuits in phasor form rather than it's time dependent form. Addition and subtraction of two phasors are faster to be done in their rectangular form. Multiplication, division, roots, and power are easier to be done in their polar form. A complex number can be expressed using polar for, rectangular form and exponential form. In our Passive RL circuit lab, we observe that voltage is leading the current (φ-θ) is negative. We observe that frequency is directly proportional to its phase difference and inversely proportional to the voltage across the inductor ( gain). In our experiment, we calculated an average 6.69 % difference. Most of the % difference is from the measurement of 1/10 cutoff frequency because the difference between two peaks are relatively small.