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Series and Parallel AC Circuits
75 questions By Tony R. Kuphaldt
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Question 40 of 75
Calculate the necessary size of the capacitor to give this circuit a total impedance (Ztotal) of 4 kΩ, at a power supply frequency of 100 Hz:
Reveal answerC = 0.476 μF
Notes:Nothing special to note here, just practice with the impedance triangle (and the capacitive reactance formula).
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Question 41 of 75
Capacitors and inductors are complementary components - both conceptually and mathematically, they seem to be almost exact opposites of each other. Calculate the total impedance of this series-connected inductor and capacitor network:
Reveal answerZtotal = 13 Ω ∠ -90o
Follow-up question: does this circuit “appear” to be inductive or capacitive from the source’s point of view?
Notes:Here, the complementary nature of inductive and capacitive reactances is plain to see: they subtract in series. Challenge your students by asking them what the total impedance of this circuit would be if the two reactances were equal.
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Question 42 of 75
Write an equation that solves for the impedance of this series circuit. The equation need not solve for the phase angle between voltage and current, but merely provide a scalar figure for impedance (in ohms):
Reveal answerZtotal = √{R2 (XL − XC)2}
Notes:Ask your students why one of the reactance terms under the radicand is positive and the other is negative. The way this equation is written, does it matter which term is negative? As your students if we would obtain the same answer if it were written as Ztotal = √{R2 (XC − XL)2} instead. Challenge them to answer this question without using a calculator!
