Phasors: Passive RL Circuit Response

We have completely finished the first part of the class, DC circuits. Now we move on to a new part of this class, AC circuits. Today we are introduced to a new powerful tool to analyze AC circuits, phasor. Phasor is a representation of a sinusoidal wave without the time dependence. Also, capacitors and inductors can also be considered as resistors with imaginary impedance. Ohm's Law still applies to AC circuits.

Then we did a lab on passive RL Circuit Response. Here is a schematic of the lab

We applied three different sinusoidal waves to the voltage input and calculated the gain and phase difference.

ω = 47krad/s

	Experimental	Theoretical	Percent Error
Angular Frequency (krad/s)	47.00	47.00	0.00%
Frequency (kHz)	7.48	7.48	0.00%
Gain	0.0149	0.015	1.28%
Phase Difference (º)	-43.1459	-45.000	4.12%

ω = 470krad/s

	Experimental	Theoretical	Percent Error
Angular Frequency (krad/s)	470.0	470.0	0.00%
Frequency (kHz)	74.8	74.8	0.00%
Gain	0.0021	0.0021	0.14%
Phase Difference (º)	-86.1859	-84.289	2.25%

ω = 4.7krad/s

	Experimental	Theoretical	Percent Error
Angular Frequency (krad/s)	4.700	4.700	0.00%
Frequency (kHz)	0.748	0.748	0.00%
Gain	0.021	0.021	2.89%
Phase Difference (º)	-4.933	-5.711	13.61%

Summary: The impedance of a resistor is R; the impedance of a capacitor is -j/ωC or 1/jωC; the impedance of an inductor is jωL. It is obvious that the impedance of a capacitor or an inductor changes when different frequency is applied. This causes the different gain and phase difference in each case. Using phasors can help us analyze AC circuits in the same way as DC circuits.