Capacitors and inductors can be used in both direct and alternating currents circuits

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Tuned circuit and power factor
Student’s Name
Institutional Affiliation
Date

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Aims
i) To estimate the value of an inductor
ii) To design, build and test a tuned filter
iii) To calculate the capacitor size needed to correct the power factor of an electrical
circuit and to test the correction
Introduction
An inductor is a simple electrical device that consists of turns of insulated copper wire
wound on a former, with a core made of a material such as soft iron. An inductor is a passive
device that is used in both alternating current and direct current applications. The core can
also be just air as is the case in inductors used for high frequency applications. The action of
an inductor is dependent on the magnetic field that develops within the core and around the
coils as they carry an electric current. The efficiency of an inductor greatly depends on the
material of the core in terms of its ability to concentrate the magnetic fields (Hurley and
Wölfle 2013). Materials that are easily magnetized are the best choices for inductor cores.
The inductor stores energy in its magnetic field. When an electric current flows through the
coils of an inductor, experiments have shown that the voltage developed across the inductor
is proportional to the rate of change of the current with respect to time.
v ∝ di
dt
v=L d i
dt
The constant of proportionality, L is known as inductance and has the unit, Henry. Inductance
can be defined as opposition offered by the inductor to the change of current flowing through

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it. The value of L depends on many factors such as the physical dimensions of the inductor
and the core material.
A capacitor, on the other hand, is a passive element that is constructed from two
conductors separated by a thin insulating medium called a dielectric. The dielectric medium
varies greatly, from the use of air as the separating medium to electrolytic solutions. This
gives rise to different types of capacitors such as air filled capacitors, electrolytic capacitors
and ceramic capacitors (Damor, 2019). Some capacitors such as electrolytic capacitors have
polarities while others are unpolarised. Unlike an inductor, a capacitor stores energy in its
electric field. According to Bird (2010), capacitors are the most commonly encountered
elements in electronic devices, besides resistors. The application of a potential difference v
across a capacitor develops opposite charges −q andq, on its plates. The stored charge is
directly proportional to the potential difference.
q ∝ v
q=Cv
The constant of proportionality, C is known as capacitance and its unit is the Farad.
Inductors, capacitors, and resistors in AC circuits
Capacitors and inductors can be used in both direct and alternating currents circuits.
However, their responses and analysis in AC circuits are more interesting and complex than
in DC circuits. Capacitors, inductors, and resistors can be combined in parallel or series to
form different types of circuits with different response characteristics in terms of parameters
such as resonance (frequency response). These include RL, RC, LC and RLC parallel and
series connections (Schulz 2010).

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Power factor and power factor correction
Different electrical loads may require different types of power. Most loads encountered today
such as transformers, motors, and light ballasts are inductive in nature (Batarseh and Wei
2011). According to Clayton (2018), inductive loads demand two types of currents. These
include the real power (working power) needed to carry out the actual task such as motion,
heat generation, and light, and the reactive power which is needed to create and sustain a
magnetic field. Real power is measured in watts while reactive power is measured in VAR
and does not perform any useful work other than circulating between the load and the power
generator. It places a heavier burden on the power supply. Real and reactive power make up
the apparent power. Power factor can be defined as the ratio of real power to apparent power
and is a measure of the effectiveness of the power usage. A high power factor indicates
efficient power utilization whereas a low power factor indicates wastage.
pf = realpower
apparentpower =cosθ
Where θ is the angle between the true and apparent power in the power triangle or the angle
by which the current lags or leads the supply voltage. If the current leads the supply voltage,
the power factor is said to be leading while a lagging current produces a lagging power factor
(Balabanian, 2012). Inductive loads produce lagging power factor while capacitive loads
produce leading power factor.
Part 1
Procedure

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i) The circuit shown in figure 1 below was designed using a resistor of 1000 Ω and
the inductor whose value was to be determined.
ii) The circuit was then connected to a variable frequency power supply as shown.
iii) Keeping the supply voltage constant, the supply frequency was varied and the
voltage across the resistor recorded
iv) The ratio of the supply voltage to the voltage across the resistor V s
V r
was then
computed and its square ( V s
V r )
2
determined for every value of frequency.
v) To determine the value of the inductor ( V s
V r )2
was plotted against the square of the
frequency to obtain a straight-line plot.
vi) The value of the inductor was then computed from the slope of the graph.
Using Kirchhoff’s voltage law, the supply voltage can be expressed as,
V s =IR+ I XL
V s =IR+ I ( 2 πfL )
V s
IR =1+ I ( 2 πfL )
IR
V s
IR = ( 2 πfL )
R +1
But IR=V r
( ( 2 πfL )
R )+1
Squaring both sides, we have,

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( V s
V r )
2
=( ( 2 πfL )
R )
2
+ 1
( V s
V r )2
=( ( 2 πL )
R )2
f 2+1
A graph of ( V s
V r )
2
against f 2 gives a straight line from which the value of the inductor L can be
calculated from the gradient of the line.
Figure 1: Circuit diagram for inductor value estimation
Results
0 10000000 20000000 30000000 40000000
0
2
4
6
8
10
12
14
16
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f(x) = 0 x + 1
f2
(VS/VR)2