How to Calculate Phasors
A phase vector, or phasor, is a representation of a sine wave whose amplitude, phase and frequency are time invariant. The projection of phasors onto the vertical axis gives their instantaneous values. They are used to analyze alternating circuits and light wave amplitudes.
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Things You'll Need
- Familiarity with the simplest AC circuit equations
- Familiary with the simplest trigonometric relations
Instructions
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1
Extend the phasor for the current amplitude. The amplitude should have an angle ωt - φ with the positive x-axis. Therefore, its projection onto the vertical axis will be I, the instantaneous current.
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2
Represent the amplitude of the potential drop across the resistor of the LCR circuit in the same direction as I, since there is no lag between the two.
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3
Add in the potential drop across the capacitor and inductor of the LCR circuit. Incorporate the fact that the current lags the inductor voltage drop and leads the capacitor voltage drop. Note that the four vectors maintain their angles with respect to each other as they rotate around the origin.
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4
Combine the two opposite vectors into one, in preparation for making a parallelogram to find the electromotive force (EMF) of the circuit.
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5
Note that the parallelogram formed by the potential-drop vectors gives the phasor of the EMF's amplitude, EM, as its diagonal.
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6
Note that the angle of the EMF amplitude is ωt. Therefore, the angle between the EMF amplitude and the current amplitude is φ.
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7
Use the Pythagorean theorem to find an algebraic relation between the three potential differences, and therefore a relation between the magnitude of the alternating EMF and the magnitude of the alternating current.
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