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Wentworth Institute of Technology
Department of Electronics and Mechanical
ELEC 195 - Circuits Theory II
Name:
Date:
Experiment 5
Using a Current Sensing Resistor to Find the Inductive and
Capacitive Load Impedance
Objective:
1. To learn how to calculate the resistance and reactance of elements using a currentsensing resistor.
2. To become familiar with the oscilloscope as a voltage-measuring instrument.
Equipment Required:
Resistor:
Capacitor:
Inductor:
Leads:
Jumpers
A breadboard
100 
1 F
10 mH
1 set of banana-to-clip leads and 2 sets of BNC-to-clip leads
Resume of Theory:
Impedance in the frequency domain is the quantity analogous to resistance, inductance
and capacitance in time domain. The imaginary part of the impedance is called reactance.
The reactance of an inductor or capacitor is a function of the applied frequency as defined by the
followings
1
 .c
X L  .L
Xc 
where
  2f
rad/s , L =the inductance (H) and C = the capacitance (F)
The inductor and capacitor impedances in rectangular forms are:
Zc = - j X c
ZL = j X L
and in polar forms
ZL = |XL|90o
Zc = |Xc|-90o
1
Note: Ideally, internal resistance of an inductor is zero; however, a real life inductor has small
resistance, and some cases the resistance is high enough that cannot be ignored. So, in this
case, the impedance of an inductor is:
ZL = RL + j XL
Where RL is the internal resistance of the inductor and X L is the inductive resistance
Procedure:
PART I:
a)
Capacitive Load
Construct the circuit shown below (Fig 4.1)
Fig. 4.1
b)
Measure the sensing resistor
Rs = ______________
c)
Set the voltage Vc to 4 Vpp and measure the RMS value of VRs
VRs = ______________
d)
Calculate VRS-pp
VRS-pp = ____________
e)
Calculate Ipp
Ipp = _______________
2
f)
Xc 
Calculate the capacitive reactance
Vcpp
Ipp
Xc (from measured values)= _________________
g)
Measure the actual capacitance of the capacitor using the bridge.
C = _____________
h)
Using the capacitance value measured in part g, calculate the capacitive reactance of the
circuit.
Xc (calculated) = ___________
i)
Compare the capacitive reactance in part f and h, and find the percentage of error
between the two values. Comment on your results.
j)
Raise the source frequency to 400 Hz, and repeat part I. Compare the new capacitive
reactance with the one found before. Comment on the results
k)
Draw the vector diagram and to find the impedance seen by the source for each
frequency.
PART II:
Inductive Load
a)
Construct the circuit shown below (Fig. 4.2).
b)
Measure the sensing resistor
Fig. 4.2
Rs = ______________
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c)
Set the voltage VL to 1 Vpp and measure the RMS value of VRs
VRs = ______________
d)
Calculate VRS-pp
VRS-pp = ____________
e)
Calculate Ipp
f)
Calculate the inductive impedance
| Z L |
Ipp = _______________
VLpp
Ipp
|ZL| (from measured values)= _______________
g)
Measure the actual inductance of the inductor using the bridge.
L = _____________
h)
Using the inductance value measured in part g, calculate the inductive reactance of the
circuit.
XL (calculated) =ω.L= ___________
Using the DMM measure the internal resistance of the inductor.
RLint = ________________
Calculate the ZL
|ZL|(calculated) = RLint + j XL =
( RLint  X L = ____________
2
2
i)
Compare the inductive impedance (ZL) in part f and h, and find the percentage error
between the two values. Comment on your results.
j)
Drop the source frequency to 1 KHz, and repeat part II. Compare the new
inductive reactance with the one found before. Comment on the results
k)
Draw the vector diagram and to find the impedance seen by the source for each
frequency.
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