6.(20 pts.) (6a)Circuit (10 pts.): A signal generator is producing a sine wave o

Question

6.(20 pts.) (6a)Circuit (10 pts.): A signal generator is producing a sine wave of amplitude 15.0 V at a frequency of f 6,000 Hz (which is NOT the resonant frequency). The generator is hooked in series with a 50 resistor, a .0027 H inductor, and a 2.0 F capacitor. Sketch this AC circuit diagram in the space below and be sure to label the parts. Use the appropriate electrical symbols for the circuit components. Questions (10 pts): Give your answers below to 3 significant figures. (a] Find the inductive reactance and the capacitive reactance at f 6000 Hz. (b) Find the total impedance Zo (C) What is the current amplitude of the circuit when it is at its resonance frequency? Hint: what is the relation between X1 and Xc at resonance? What does this imply for the value of the impedance which determines the current I)? (d) What is the voltage amplitude across the inductor at the resonance frequency?

Explanation / Answer

6. (A) inductive reactance, XL = 2 pi f L

XL = 2 x pi x 6000 x 0.0027 = 102 ohm

capacitive reactance , Xc = 1/ (2 pi f C )

Xc = 1/ (2 x pi x 6000 x 2 x 10^-6)

Xc = 13.3 ohm

(b) Z = sqrt[ R^2 + (XL - Xc)^2]

R = 50 ohm

so Z = 102 ohm

(c) at resonance frequency, XL =Xc

so Z = R

I = V / Z = 15 / 50 = 0.300 A  

(d) at resonance,

wL = 1/wC => w = 1 / sqrt(0.0027 x 2 x 10^-6) = 13608 rad/s

xL = wL = 0.0027 x 13608 = 36.7 ohm

VL = 36.7 x 0.300 = 11.0 Volt

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