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Trigonometry for AC Circuits
23 questions By Tony R. Kuphaldt
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Question 10 of 23
A parallel RC circuit has 10 μS of susceptance (B). How much conductance (G) is necessary to give the circuit a (total) phase angle of 22 degrees?
Reveal answerG = 24.75 μS
Follow-up question: how much resistance is this, in ohms?
Notes:Ask your students to explain their method(s) of solution, including any ways to double-check the correctness of the answer.
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Question 11 of 23
The Pythagorean Theorem is used to calculate the length of the hypotenuse of a right triangle given the lengths of the other two sides:
Write the standard form of the Pythagorean Theorem, and give an example of its use.
Reveal answerI’ll let you research this one on your own!
Follow-up question: identify an application in AC circuit analysis where the Pythagorean Theorem would be useful for calculating a circuit quantity such as voltage or current.
Notes:The Pythagorean Theorem is easy enough for students to find on their own that you should not need to show them. A memorable illustration of this theorem are the side lengths of a so-called 3-4-5 triangle. Don’t be surprised if this is the example many students choose to give.
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Question 12 of 23
Use the “impedance triangle” to calculate the impedance of this series combination of resistance (R) and inductive reactance (X):
Explain what equation(s) you use to calculate Z.
Reveal answerZ = 625 Ω, as calculated by 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.
