Download LAB 12 AC Circuits

LAB 12
AC Circuits
OBJECTIVES
1. Observe the frequency behavior of resistor, capacitors, and inductors.
2. Note that the reactance of an inductor increases linearly with increase in frequency.
3. Confirm that the reactance of a capacitor decreases nonlinearly with increase in
frequency.
EQUIPMENT
DataStudio (Scope & Voltage Sensors), Function Generator, 4.7k resistor, decade
resistor, 3400 turn coil, 0.22 F capacitor, DMM, and Leads.
THEORY
The reactance of a resistor XR is unaffected by frequency (except for extremely high frequencies):
XR  R
The reactance of an inductor XL is linearly dependent on the frequency applied. That is,
if we double the frequency, we double the reactance, as determined by
XL  L  2πf  L
For very low frequencies, the reactance is correspondingly very small, whereas for
increasing frequencies, the reactance will increase to a very large value. For DC
conditions, we find that XL = 2(0) L is 0, corresponding with the short-circuit
representation we used in our analysis of DC circuits. For very high frequencies, XL is so
high that we can often use an open-circuit approximation.
The reactance of a capacitor XC is inversely proportional the frequency applied:
XC 
1
1

C 2πf  C
At low frequencies, the reactance of a capacitor is quite high, often permitting the use of
an open-circuit equivalent. At higher frequencies the reactance of a capacitor decreases in
a nonlinear manner. At very high frequencies, the capacitor can be approximated by a
short-circuit equivalency.
PROCEDURE
Part 1: Frequency Response of a Resistor
a. Construct a circuit consisting of a 4.7k resistor and the decade resistor set to 500 
in series with a function generator. The decade resistor will serve as the “sensing”
resistor used to measure the current through the circuit. Use a DMM to measure the
actual resistances of the 4.7k resistor and the decade resistor.
b. Set the output of the function generator to sine wave and adjust the amplitude of the
sine wave so that is approximately 2.0 V using the scope display on Capstone.
c. Set up Capstone so that it shows the voltage drops across both the 4.7k resistor and
the 500 decade resistor simultaneously on the scope display.
d. Adjust the frequency of the sine wave output from the Function Generator until it is
approximately 100 Hz.
e. Measure the voltage drop across the (i) 500 “sensing” resistor (VSR (t)) and (ii) 4.7k
resistor (VR(t)) as a function of time.
f. Calculate the experimental value of R using Ohm's law: R = VR/IR.
g. Repeat steps (d) – (g) for the other frequencies listed in Table 1.
12-1
h. Based on the results of Table 1, is the resistance of the resistor independent of
frequency for the tested range?
Data Analysis
 Calculate the theoretical resistive reactance XR,thy by averaging over all of the
measured values of XR,expt in Table 1.
Part 2: Frequency Response of an Inductor
a. Replace the 100 of Part 1 with a 3400 turn inductor and measure its inductance L
with a DMM.
b. Repeating the steps from Part 1 and complete Table 2. That is, measure the voltage
drop across the (i) 500 “sensing” resistor (VSR (t)) and (ii) inductor (VL(t)) as a
function of time.
Data Analysis
 Calculate the (i) experimental inductive reactance XL,exp and (ii) theoretical inductive
reactance XL,thy at each frequency and insert the values in Table 2. Be sure to use the
measured value of the inductance for the theoretical value.
 Does the current in the circuit decrease as the frequency goes up? Explain what is
happening.
 How do the experimental and theoretical values of XL compare?
 Plot XL,expt versus frequency using Excel. Determine the experimental inductance Lthy
using your slope from your plot. Compare it with the measured value. How do they
compare?
Part 3: Frequency Response of an Inductor
a. Replace the 100 of Part 1 with a 0.22 F capacitor and measure its capacitance C
with a DMM.
b. Repeating the steps from Part 1 and complete Table 3. That is, measure the voltage
drop across the (i) 500 “sensing” resistor (VSR (t)) and (ii) capacitor (VC(t)) as a
function of time..
Data Analysis
 Calculate the (i) experimental capacitive reactance XC,exp and (ii) theoretical capacitive
reactance XC,thy at each frequency and insert the values in Table 3. Be sure to use the
measured value of the capacitance for the theoretical value.
 Does the current in the circuit increase as the frequency goes up? Explain what is
happening.
 How do the experimental and theoretical values of XC compare?
 Plot XC,expt versus 1/frequency using Excel. Determine the experimental inductance
Cthy using your slope from your plot. Compare it with the measured value. How do
they compare?
 Plot all three reactance’s (R, XL, XC) vs ω on one single plot. What are the
differences?
12-2
Table 1: Resistor
f(Hz)
100
200
300
500
800
1000
VR
VSR
IR = VSR/RSR
Rexpt = VR/IR
Rthy
% diff
Table 2: Inductor
f(Hz)
100
200
300
500
800
1000
VL
VSR
IL = VSR/RSR
XL,exp = VL/IL
XL,thy = 2fL
% diff
Table 3: Capacitor
f(Hz)
100
200
300
500
800
1000
VC
VSR
IC = VSR/RSR
XC,exp = VC/IC
XC,thy = 1/(2fC)
% diff
12-3