Скачать или смотреть Visual AC circuit physics: how phasors generate voltage waveforms in an RLC circuit.

How can rotating vectors represent sinusoidal voltage functions in an AC circuit?

The answer is that we take the horizontal projections of the rotating vectors to transform circular motion into sinusoidal functions! These special vectors are called "phasors", because they allow us to use simple vector addition to add multiple sinusoidal functions differing in phase.

In this 4K animation, we view four voltage phasors in a phasor diagram, corresponding to the voltage across a resistor, inductor and capacitor in a series RLC circuit. The fourth phasor is the net voltage phasor across the combination, which was obtained as the vector sum of the other three phasors.

We include a color key to illustrate how phasors generate four different voltage waveforms for the RLC circuit:

1. Voltage across the resistor: IRcos(wt), where R is the resistance.
2. Voltage across the inductor: IX_Lcos(wt+pi/2), where X_L is the inductive reactance.
3. Voltage across the capacitor: IX_Ccos(wt-pi/2), where X_C is the capacitive reactance.
4. Net voltage (or voltage of the AC power source): IZcos(wt+phi), where Z is the total impedance of the circuit and phi is the phase angle, calculated as arctan((X_L-X_C)/R).

This video is the culminating animation from my short series on AC circuit phasor analysis, which you can find here:

Part 1: the current phasor and the voltage phasor for a resistor:
👉    • The current phasor and resistor voltage ph...  

Part 2: the voltage phasor for an inductor:
👉    • The inductor voltage phasor and inductive ...  

Part 3: the voltage phasor for a capacitor:
👉    • The capacitor voltage phasor and capacitiv...  

Part 4: phasor analysis of the RLC circuit:
👉    • RLC series circuit phasor analysis, impeda...  

Part 5: RMS values for current and voltage - full calculus derivations.
👉    • RMS values for current and voltage - full ...  

Part 6: Power calculations for inductors, capacitors and resistors.
👉    • Power in AC circuit elements - full calcul...  

Part 7: Power and the power factor in a general AC circuit. [TBA]

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

#physics #ACcircuits #phasors