I'm taking AC circuits right now and we just started converting polar to rectangular and vice versa and this video was REALLY helpful for understanding how to work with real and imaginary components of voltage and current. The concept of phase angles really clicked just watching you work the problems. I will no longer be one of the 'lost ones' when I walk into class next week. Thank you for making this video.
I remember being confused, 40 years ago, when I learned that capacitance in series is not additive, and that inductance in parallel is not additive. What I failed to consider is how this is elegantly accounted for by the way we calculate impedance, with capacitance being in the denominator of Z = 1/(2*pi*f*C), and inductance being in the numerator of Z=2*pi*f*L. So, once you calculate your individual impedance numbers, don't let those details confuse you. Once impedance conversion is done, it is simply a matter of rolling through and trusting the math, letting phase angle take care of the details.
The 'j' before the 40 denotes that the number is an imaginary number. In the real/imaginary plane, the horizontal axis is deemed the real axis and the vertical axis is deemed the imaginary axis. An impedance of 40 Ohms 90 degrees would be a vector pointing straight up which is all in the imaginary axis, so it has a value of 40 imaginary Ohms or j40 Ohms.
