Before you attempt to do this pre-lab exercise, you must read the Basic Theory s

Question

Before you attempt to do this pre-lab exercise, you must read the Basic Theory sections in the Resonance" installment of the laboratory manual Alice and Bob are studying an RLC circuit. They set up the circuit shown to the right: Alice sets the frequency, f, of the sine wave voltage source used in this circuit to be 318.3 Hz and she measures the resistance of the resistor, R, to be 10.0Kn, while Bob measures the amplitude of the voltage across R, Ve.to be v 2.50 volts 1. Calculate I, the amplitude of the current in this circuit Bob measures the amplitude of voltage across the capacitor to be 1.25 volts. 2. Calculate Xc, the reactance of the capacitor. 3. Calculate C, the capacitance of the capacitor. Alice measures the amplitude of voltage across the inductor to be 5.00 volts. 4. Calculate Xi, the reactance of the inductor. 5. Calculate L, the inductance of the inductor. 6. Calculate the resonance frequency for this circuit.

Explanation / Answer

a)

I=VR/R =2.5/10000 =2.5*10-4 A

b)

Capacitive reactance

XC=VC/I =1.25/2.5*10-4 =5000 ohms

c)

Capacitance of the capacitor

C=1/2pifXC =1/2pi*318.3*5000

C=1.00003*10-7 F

d)

Inductive reactance

XL=VL/I =5/(2.5*10-4) =20000 ohms

e)

Inductance

L=XL/2pif =20000/2pi*318.3

L=10.0003 H

f)Resoance frequency

fr=1/2pisqrt(LC)=1/2pisqrt[10.0003*1.00003*10-7)

fr=159.15 Hz

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