The capacitor voltage phasor and capacitive reactance. [AC circuit physics]

Starting with the analysis of a simple capacitor circuit, we find the capacitor voltage phasor and show why it lags the current phasor!

In this video, we complete our phasor analysis toolkit by developing the voltage phasor for a capacitor and viewing an animation of capacitor voltage phasor along with the current phasor as the horizontal projections of these phasors generate the sinusoidal functions they represent. This completes our phasor analysis toolkit, because now we have phasors for resistors, inductors and capacitors: the next project is to solve the LRC series AC circuit!

We derive the voltage phasor for a capacitor by applying KVL to a simple AC capacitor circuit, taking the time derivative to express dv/dt in terms of i, then subbing in the standard AC current function i(t)=Icos(wt) and integrating. This gives us a voltage function of I/(wC)*sin(wt).

We re-express this sinusoidal function as a phase-shifted cosine AND we introduce the capacitive reactance X_C=1/(wC). The point of the capacitive reactance is to build an Ohm's Law - like relation for voltage and current amplitude, and since V=(1/wC)*I, we see that the capacitive reactance 1/(wC) plays the role of resistance, and we discuss the physical meaning of its frequency-dependence.

Finally, we show the static phasor diagram for the capacitor voltage and current phasors, then wrap it up with an animation of the rotating phasors and the sinusoidal functions they generate.

This video is part of a short series on AC circuits and phasor analysis:

Part 1: the current phasor and the voltage phasor for a resistor:
👉 https://www.youtube.com/watch?v=T1E9StnhSNE

Part 2: the voltage phasor for an inductor:
👉 https://www.youtube.com/watch?v=DnUa_i_M0FE

Part 3: the voltage phasor for a capacitor:
👉 https://www.youtube.com/watch?v=jlwKDnAW-7I

Part 4: phasor analysis of the RLC circuit:
👉 https://www.youtube.com/watch?v=gCliWIraCaU

Part 5: RMS values for current and voltage - full calculus derivations.
👉 https://www.youtube.com/watch?v=6HiiPLn-vAI

Part 6: Power calculations for inductors, capacitors and resistors.
👉 https://youtu.be/T08BYGMg9lY

Part 7: Power and the power factor in the RLC series circuit.
👉 https://youtu.be/RWS1q0K0FYM

Part 8: Resonance in the RLC circuit + RLC power calculations. [TBA]

#physics #ACcircuits #phasors

Видео The capacitor voltage phasor and capacitive reactance. [AC circuit physics] канала Zak's Lab