Excellent video. This directly relates to power systems I'm designing so it's great to have more detailed breakdowns available. It would be great to see more content on combined systems where capacitive reactance is part of the distributed system on a real low impedance power line.
Something doesn't sit right with me about the visualization at 3:20. When a current is lagging with respect to a voltage or vice versa, that means that, on the time axis, they are shifted. But, on the representation, both current and voltage always achieve their zeros at the same instant. The lag was shown on a dimension perpendicular to time. When you represent AC signals with complex numbers, you don't fix the fase and vary the magnitude, you have to fix the magnitude and vary the phase, such that the signal rotates around the time axis. The actual signal you get in the real world is the real part of that complex function.
if the current is a general function other than "cos" for instance let's say " I = exp(-t) " do you think that the voltage " V = exp(-t) * Z * exp(j theta) " should be shifted on time axis while rotating theta radians in the complex plane?
@TheSiGuy Impedance is frequency dependent, that is, it only works for signals containing a single frequency, which is the case for the cossine. For any signal containing more frequencies or non-periodic functions (like the exponent), you can define the impedance on the s domain via laplace transform. The thing is, you cannot mix the s domain and the time domain.
@@victorscarpes OK, thank you for highlighting that impedance is frequency dependent :) Let's focus on the formula. does that formula " cos(t) Z exp(j theta) " has any time shift as theta varies?
Excellent video. This directly relates to power systems I'm designing so it's great to have more detailed breakdowns available. It would be great to see more content on combined systems where capacitive reactance is part of the distributed system on a real low impedance power line.
Something doesn't sit right with me about the visualization at 3:20. When a current is lagging with respect to a voltage or vice versa, that means that, on the time axis, they are shifted. But, on the representation, both current and voltage always achieve their zeros at the same instant. The lag was shown on a dimension perpendicular to time. When you represent AC signals with complex numbers, you don't fix the fase and vary the magnitude, you have to fix the magnitude and vary the phase, such that the signal rotates around the time axis. The actual signal you get in the real world is the real part of that complex function.
if the current is a general function other than "cos" for instance let's say " I = exp(-t) " do you think that the voltage " V = exp(-t) * Z * exp(j theta) " should be shifted on time axis while rotating theta radians in the complex plane?
@TheSiGuy Impedance is frequency dependent, that is, it only works for signals containing a single frequency, which is the case for the cossine. For any signal containing more frequencies or non-periodic functions (like the exponent), you can define the impedance on the s domain via laplace transform. The thing is, you cannot mix the s domain and the time domain.
@@victorscarpes OK, thank you for highlighting that impedance is frequency dependent :) Let's focus on the formula. does that formula " cos(t) Z exp(j theta) " has any time shift as theta varies?
@@TheSiGuyEN no, it does not.
Awesome video, working on that active power on an induced load
This AC videos are so cool 😮
❤