Phasors
Phasors of Purely Resistive, Inductive and Capacitive Circuits
Learning Objectives:
- Explain what is a phasor diagram.
- Explain and determine the characteristics of a pure resistive, pure inductive and pure capacitive circuit.
Phasor Diagram
Phasor
- Used to represent sinusoidal functions.
- Useful in showing the relationship V$_m$ over time of various quantities v 2 $\pi$ ft + $\phi$ (such as current and voltage).
- A phasor is a vector (i.e. described by polar coordinates length and angle) with
- length equal to amplitude of function (V$_m$) $v = V_m \sin(2 \pi ft+\phi)$
- angle equal to argument ($\theta$)
- height equal to value of function ($\phi$)
Phasor Diagram Pure Resistive Circuit:
- The voltage across the resistor oscillates in phase with the emf of AC generator.
- Current and voltage across the resistor are in phase:
- They peak and trough at the same time, and both are zero at the same times as well.
Phasor Diagram Inductor:
- Passive electrical device that stores energy in a magnetic field, by combining the effects of many loops of electric current
- Change in current will induce a an opposing emf in an inductor
- Inductance L is a physical characteristic of an inductor (unit is Henry, H).
- Inductance relates the induced emf of an inductor to the rate of change of current
Д.Ильин, CC0, via Wikimedia Commons
Phasor Diagram Pure Capacitive Circuit:
- Current starts at a maximum while the voltage across the capacitor is zero, since it is initially uncharged
- When the current reaches zero, the capacitor plates are fully charged, and the magnitude of the voltage across it is at a maximum
- The current reaches a peak earlier in time than the potential difference does.
- Current leads voltage by 90°
Phasors of Mixed Circuits
R-L circuit:
- Current lag behind voltage
- Power factor is lagging
- Phase angle is negative.
- Current leads the voltage.
- Power factor is leading.
Solved Example: 9244-01
While drawing vector diagram for a series circuit, the reference vector is?
A. Voltage
B. Current
C. Power
D. Phase angle
Correct Answer: B
Solved Example: 9244-02
The power factor of a series LCR circuit at resonance is:
A. 0.707
B. 0.50
C. 0.00
D. 1.00
Correct Answer: D
Solved Example: 9244-03
Magnitude of current at resonance in R-L-C circuit:
A. Depends upon the magnitude of R
B. Depends upon the magnitude of L
C. Depends upon the magnitude of C
D. Depends upon the magnitude of R, Land C
Correct Answer: A