Скачать или смотреть RLC series circuit phasor analysis, impedance and phase angle. [AC circuit physics]

What happens when we combine a resistor, inductor and capacitor in an AC series circuit? Using the phasor representation of the voltage wave functions for the resistor, inductor and capacitor, we use the geometry of phasors to relate the total voltage at the power source to the total current flowing in the circuit, and we find the total impedance of the circuit and the phase angle between the net voltage and the current flowing in the circuit. To pull it all together geometrically, we view an animation of the rotating phasor diagram along with all the voltage waveforms generated by taking the horizontal projections of the phasors.

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00:00 Introductions and rotating phasor animation: waveform spaghetti.

01:14 KVL analysis of the RLC series circuit (or LRC series circuit) + writing down v(t), the net voltage function, in terms of the voltage functions for the resistor, inductor and capacitor.

04:13 The phasor representation of our circuit elements: we review the phasor representation of the resistor voltage function, the inductor voltage function and the capacitor voltage function. Each of the voltage functions for these AC circuit elements is generated by taking the x-component of its phasor.

05:55 Vector math: the sum of the x-components is equal to the x-component of the vector sum! Thankfully, this is how vectors work, and this means we can vector add the phasors geometrically, then take the x-component of the vector sum in order to find the sum of all the voltage functions.

07:42 Key results found by adding the phasors geometrically: we vector-add head to tail and find the resultant voltage phasor for the RLC circuit. We then express this vector sum in polar form, using a voltage magnitude V=Isqrt(R^2+(X_L-X_C)^2). We define impedance as Z=sqrt(R^2+(X_L-X_C)^2), and this means we have an Ohm's Law style relation between voltage amplitude and current amplitude: V=IZ. In addition, we find the phase angle for the net voltage phasor, and that's phi=arctan((X_L-X_C)/R). Taking the horizontal projection of the net voltage phasor, we get v(t)=IZcos(omega*t+phi), and this allows us to see the relation between net voltage and total current waveforms for the RLC series circuit.

13:21 Victory lap! We view the composite animation of the rotating phasor diagram and the waveforms it generates. Three sinusoidal functions for the resistor, inductor and capacitor conspire to form the single net voltage waveform as the phasor diagram rotates. Now you really understand alternating current waveform spaghetti!

Part of a short series on AC circuits and phasor analysis:

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 the RLC series circuit.
👉    • Power and the power factor in the series R...  

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

#physics #ACcircuits #phasors