I have additional questions for 23.33 The original question states, A 10.0ohm re
ID: 2097745 • Letter: I
Question
I have additional questions for 23.33
The original question states, A 10.0ohm resistor, a 12.0uF capacitor, and a 17.0mH inductor are connected in series with a 155V generator. a) At what frequency is the current maximum? b) What is the maximum value of the rms current? for part a and b I got f=352.37Hz, b) I=15.5A. The additional questions are as follows 1.) At this "resonance frequency", what is the amplitude of the voltage across the resistor, capacitor, and inductor? 2.) At resonance, what is the average power disipated by the resistor? 3.) At resonance what is the peak energy stored in the inductor and the capacitor? 4.) Solve for the amplitude of the current flowing through the circuit when: (a) the frequency of the generator is 300Hz (b) the frequency of the generator is 400Hz (c) The frequency of the generator is 500Hz. Can anyone please show me step by step how to solve these problems? I really need to see the steps so that I can fiqure this out.
Explanation / Answer
f = 1/2pisqrt(LC)
=> f =1/2*3,14*sqrt(12*10^-6*17*10^-3)
f=1/2*3.14*4.5166359162*10^-4 = 352.553696473 Hz ANSWER
i rms = 155/10 = 15.5 A ANSWER
1) across resistor amplitude = 155*sqrt(2) = 219.2031022 V
across capacitor = 219.2031022 V
across inductor = -219.2031022 V
2) avg power = I^2R = 15.5*15.5*10 = 2402.5 W
3)peak energy = 0.5cv^2 = 6*10^-6 * 155*155*2 = 0.2883 J
4)
a) i = 155/sqrt(10^2+ (2*3.14*17*10^-3 -1/2*3.14*12*10^-6)^2)
=> i = 155/sqrt(10^2+ (0.10676 -10013269.639066)^2)
=> i= 1.5479459481226*10^-5 ANSWER
B)i = 155/sqrt(10^2+ (2*3.14*300*17*10^-3 -1/2*3.14*300*12*10^-6)^2)
=> i = 155/sqrt(10^2+ (32.028 -44.23213022)^2)
=> i= 9.823894 ANSWER
c)i = 155/sqrt(10^2+ (2*3.14*400*17*10^-3 -1/2*3.14*400*12*10^-6)^2)
=> i = 155/sqrt(10^2+ (42.704 -33.174097664)^2)
=> i= 13.813726453557 ANSWER
d) i = 155/sqrt(10^2+ (2*3.14*500*17*10^-3 -1/2*3.14*500*12*10^-6)^2)
=> i = 155/sqrt(10^2+ (53.38 -26.5392781)^2)
=> i= 5.41143475761 ANSWER
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