5.(10 pts.) In the experiment \"Magnetic Fields and Induction,\" you are asked t

Question

5.(10 pts.) In the experiment "Magnetic Fields and Induction," you are asked to compare the measured magnetic field of the coil to that calculated according to an equation from your textbook. Describe the possible sources of experimental error which might result in discrepancies between the measured and calculated values. 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 (6b) Questions (10 pts): Give your answers below to 3 significant figures. (a) Find the inductive reactance and the c (b) Find the total impedance Z of the circuit (XFOL; Xc (oC)1). (c) What is the current amplitude of the circuit when it is at its resonance frequency? apacitive reactance at f = 6000 Hz. (Hint: what is the relation between X and Xc at resonance? What does this imply for the value of the impedance which determines the current 1)? (a) Whatis the voltage amplitude acros he uctor at the resonance freguenay/

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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