Phasor Analysis of AC Circuits

Luckily, the techniques employed for DC circuit analysis can be reused for the AC circuits by following the procedure outlined given below:

1. Replace the sinusoidal voltages and currents, v and i by their phasors respectively.

2. Replace linear circuit elements R, L and C by their respective impedances R, jωL and -j/ ωC .

3. Use DC circuit laws redefined for the AC circuits below to evaluate the required voltage and current phasors. Complex algebra will have to be used to simplify the equations.
 
4. Convert the voltage and current phasors back to the sinusoidal form by using the techniques learned in previous section.

Example

Use phasor analysis to determine the voltage across the terminals a and b in the circuit diagram of Drawn below

In phasor form, the supply voltage can be given by
 

The 1Ω resistance and 1 H inductance is combined into a single impedance Z1. Likewise the 2 Ωresistance and 1 F capacitor can be added to form Z2 as shown in the Figure below

Steps 1 and 2 of AC circuit analysis have now been completed whereas step 3 entails the use of one of the circuit laws. As both Z₁ and Z₂ are in series with the voltage source, thus VDR can be applied to determine the voltage across Z₂ which is the voltage across the terminals a and b.

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