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Trigonometry for AC Circuits
23 questions By Tony R. Kuphaldt
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Question 22 of 23
Use the “impedance triangle” to calculate the necessary reactance of this series combination of resistance (R) and capacitive reactance (X) to produce the desired total impedance of 300 Ω:
Explain what equation(s) you use to calculate X, and the algebra necessary to achieve this result from a more common formula.
Reveal answerX = 214.2 Ω, as calculated by an algebraically manipulated version of the Pythagorean Theorem.
Notes:Be sure to have students show you the form of the Pythagorean Theorem, rather than showing them yourself, since it is so easy for students to research on their own.
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Question 23 of 23
A parallel AC circuit draws 100 mA of current through a purely resistive branch and 85 mA of current through a purely capacitive branch:
Calculate the total current and the angle Θ of the total current, explaining your trigonometric method(s) of solution.
Reveal answerItotal = 131.2 mA
Θ = 40.36o
Follow-up question: in calculating Θ, it is recommended to use the arctangent function instead of either the arcsine or arc-cosine functions. The reason for doing this is accuracy: less possibility of compounded error, due to either rounding and/or calculator-related (keystroke) errors. Explain why the use of the arctangent function to calculate Θ incurs less chance of error than either of the other two arcfunctions.
Notes:The follow-up question illustrates an important principle in many different disciplines: avoidance of unnecessary risk by choosing calculation techniques using given quantities instead of derived quantities. This is a good topic to discuss with your students, so make sure you do so.
