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w. L. 20. (12 points) In the RLC circuit above assume that R-2.00 ?, 1-100 mil,

ID: 2036885 • Letter: W

Question

w. L. 20. (12 points) In the RLC circuit above assume that R-2.00 ?, 1-100 mil, C 0.1 ?, and the power source has a constant 20 V and variable frequency f (a) (4 points) For frequency f-50 Hz, calculate impedance Z of the circuit (b) (3 points) At some frequency Jo, an amplitude of the current through the resistor is maximal. What is this frequency? (e) (3 points) What is the impedance Z of the circuit for that frequeney, fo, and how does it compare with R? (d) (2 points) If you double the frequency of the power source to 2 fo, what happens to i. capacitive reactance of the circuit? (increases, decreases, stays the same) ii. inductive reactance of the circuit? (increases, decreases, stays the same)

Explanation / Answer

a) Impedence Z = ( (Xc-Xl)2 + R2 )1/2
Xc = 1/2 pi f C = 31847 ohm    ....1
Xl = 2 pi f L = 31.4 ohm   ......2
R = 2 ohm
Z = ( (31847-31.4)2 +22)1/2
   = 31816 ohm

b) For maximum curent , frequency
fo = 1/ 2 pi (LC)1/2
     = 1592 Hz

c) At frequency fo , Xc = Xl
Hence Z = R = 2 ohm

d) From equation 1 , with increase in frequency there is decrease in capacitive reactance
and from equation 2 , with increase in frequency there is increase in inductive reactance