20: Phasors - Passive RL Circuit Response

INTRO: Today we were reintroduced to the familiar concept of phasors. Phasors were introduced to us in the prior 4B class as a way to simplify working with circuits with oscillating voltages. In other words, phasors are synonymous with working with AC circuits. They are a complex number that is composed of a real and imaginary part.


Below is visual representation of the phasor as cartesian axes. The x-axis represents the real axis, while the y axis is the imaginary axis.
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Below we began working with converting values from the time-domain to the polar/phasor domain. Using relationships we rewrite the voltage and then find the current doing mathematical operations in the phasor domain.

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Below is another representation of circuit values in the phasor domain. We do the opposite in this exercise as we go from the phasor domain to the time domain. While doing multiplication and division is simpler in the phasor domain, doing addition and subtraction is easier in the time domain.


LAB: PHASOR
In today's lab we built a RL circuit and sent a sinusoidal input and observed the circuit response. However, instead of working in the time domain to describe and evaluate the circuit we will do so in the phasor domain.


Below is a visual representation of what we will be doing in this lab.


Below is a pre-lab where we calculated circuit values in the phasor domain. For three different frequencies we calculated the gain, as well as the accompanying phase change. As to be expected, we will be comparing these to the experimental values at the end of the lab.


As stated above, the circuit was composed of a resistor as well as an inductor. We hooked it up so we could also send a voltage through the circuit when need be.


Below are the graphs of the RL circuit during the three different scenarios.




To conclude our lab I made a graph summarizing the calculated and experimental data. As the table shows, the calculated and experimental are reasonably close, resulting in a percent error less then 6% in every category.