Question

Multiple Choice Problem 22.04



A series R-L-C ac circuit with a sinusoidal voltage source of angular frequency w has a total reactance X .








Part A

If this frequency is tripled, the reactance becomes? A. 3X B. 9X C. 10/3X D. 8/3X E. none of the above

Answer 1

\[reactance=\omega L-\frac{1}{\omega C}=\frac{\omega L \omega C-1}{\omega C}\]

Answer 2

I don't understand...this seems unrelated... That isn't one of the choices 3X, 9X, 10/3X,8/3X or none of the above

Answer 3

I mean it deals with reactance but I have no values

Answer 4

If the frequency is tripled
\[reactance=3\omega L-\frac{1}{3\omega C}=\frac{3\omega L 3\omega C-1}{3\omega C}=\frac{9\omega L\omega C-1}{3\omega C}\]

Answer 5

so it is none of the above?

Answer 6

When the two outcomes are compared choice E is the correct one.

Answer 7

Oh it was wrong

Answer 8

Well it was 8/3 X

Answer 9

@lauren_hicks Was a proof of this answer given?

Answer 10

@lauren_hicks The answer you posted as correct is incorrect. As proof of this consider the case of series resonance where the angular frequency is such that the magnitudes of the capacitive reactance and the inductive reactance are equal. In this case the total reactance X = 0. If the frequency is then tripled the total reactance cannot then be: 8/3 X = 8/3 * 0 = 0

Answer 11

Well no proof was given but thanks anyway..it is still what they counted as correct

Answer 12

Thank you for feedback. Sorry to hear that an incorrect answer was given. Is it possible to ask for a proof?

Answer 13

No, not that I know of

Answer 14

Unfortunate :(