Introduction
A series connected RL circuit is one in which a resistor and a inductor are connected in series. Both
these components contribute towards the slowing down of electric current flowing through the
circuit. According to the laws of Lenz and Faraday, an inductor opposes any change in the amount of
current flowing through it. If these components are plugged into an AC circuit, they will resist or
impede the current flowing through it. All these components contribute to the total impedance of
the circuit. Impedance can be defined as the amount of resistance that a component offers to the
current in a circuit at a specific frequency.
Just like resistance, impedance also has the units of Ohms, however, there are differences between
the two. The resistance of the resistor is independent of the frequency of the current. On the
contrary, the impedance of an inductor (and/or capacitor) varies with the signal’s frequency [1]. In a
DC circuit there is no difference between impedance and resistance. It can be thought of as
impedance with a zero-phase angle.
The aim of this experiment was to use the oscilloscope and multimeter to make electrical
measurements on a series-connected single phase RL load, to observe experimentally the effect of
ABSTRACT
an AC circuit and also to verify experimentally that the magnitude of the impedance, Z, is given by
The experiment was conducted in order to better
the relation
understand the effect of having an inductor
connected in series with a resistor. The effect of
an AC circuit was experimentally observed, and
Where R is the resistance and XL is the inductive reactance in the circuit.
the total impedance was calculated.
Z = (R2+XL2)1/2
University of Botswana Faculty of Engineering and
Technology Department of Electrical Engineering
BEng Level 200 – Course EEB 241
INVESTIGATING THE IMPEDENCE OF A SERIES
CONNECTED RL LOAD
KUTLO MOSOLE : 201404817
Kutlo Mosole
201404817
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TABLE OF CONTENTS
THEORY…………………………………………………………………………………………………………2
RESULTS AND ANALYSIS………………………………………………………………………………..3
DISCUSSION …………………………………………………………………………………………………4
CONCLUSION………………………………………………………………………………………………..5
REFERENCES………………………………………………………………………………………………….6
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Theory
Input Signal
Figure 1; RL circuit
The reactances and resistances are all at right angles to each other. To find the total
impedance in the circuit the vectors must all be added up. In this experiment only the
inductor and the resistor were used.
To find the inductive reactance or impedance of the inductor we use the formula
XL = 2πfL
Where XL is the impedance in Ohms
f is the frequency in Hz
and L is the inductance in H
The magnitudes of Z, XL and V resulting from the circuit shown in figure 1 are respectively:
Z = R2 + X L2
X L = 2fL
V = VR + VL2
2
relationship: tan  =
with the circuit phase angle  given through the trigonometric
XL
R
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Results and Analysis
Table
Frequency = 100Hz-100Hz
Resistance = 100Ω
Inductance = 30mH
Frequancy(Hz) RMS
Voltage
AB (mV)
100
1309.8
250
3014.3
500
4849.7
750
5765.7
1000
6246.6
TOTAL
AVERAGE
RMS
Voltage
BC (mV)
6948.7
6396.4
5145.8
4093.4
3313.6
RMS
Current
(mA)
69.487
63.964
51.458
40.934
33.136
Calculated
Impedence
(Ω)
101.76
110.55
137.41
173.16
213.38
147.25
Calculated
Current
(mA)
69.49
63.96
51.46
40.84
33.14
51.78
Phase
Angle
(degree)
10.7
25.2
43.3
54.7
90.0
Sample Calculations
RMS VoltageTOTAL = √(𝑉²AB + V²BC ) = √(1309.82 + 6948.72 ) = 7071.1 V
XL = 2πfL = 2π(100)(30 x 10-3) = 18.85 Ω
Z = √ (R2+XL2) = √ (1002+18.852) = 101.76Ω
I = VTOTAL / Z = 7071.1V/101.76 Ω=69.49A
Phase Angle = tan-1(XL/R) = tan-1(18.85/100)= 10.67O
Power Factor = cos(10.67o)= 0.98
ANALYSIS
The resistance is independent of frequency; so, if frequency increases or decreases,
resistance remains constant. The formula for inductive reactance is X L = 2πfL. So, if
frequency increases, inductive reactance XL also increases and if inductive reactance
increases, total impedance of circuit also increases and this leads to variation in phase angle
θ with frequency. So, in series RL circuit if frequency increases,
1. Inductive reactance also increases as it is directly proportional to frequency.
2. Total impedance Z increases hence a decrease in current.
3. Phase angle θ increases.
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4. Resistance remains constant.
DISCUSSION
As seen from the results above, we can see that just as DC circuits, voltage divides for
components in series according to the ratio of their respective resistance/impedances. The
magnitude of the calculated inductive reactance(18.85 Ω) was very small as compared to
that of the resistance(100 Ω). This yielded a very small phase angle(10.7o) which in turn
yielded a power factor very close to one as the value of the total impedance was close to
that of the resistance. Having a power factor close to one shows that the system was highly
efficient as the real power is far much greater than the apparent power.
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Conclusion
The magnitude of impedance is indeed given by the relation Z = (R2 + XL2)0.5 as we could see
the Impedence linearly increasing as inductance increased.In case of pure resistive circuit,
the phase angle between voltage and current is zero and in case of pure inductive circuit,
phase angle is 90o but when we combine both resistance and inductor, the phase angle of a
series RL circuit is between 0o to 90o.
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References
[1] Stephen L. Herman (2011), Alternating Current Fundamentals, 8th edition, Delmar Centage
Learning, Clifton Park, USA
[2] Levent Sevgi (2017), A Practical Guide to EMC Engineering, 2nd edition, Artech House Publishers,
Norwood, USA