Practical number 5: Alternating current circuits and phasors

A practical-report submitted for the partial fulfilment of the requirements for the
degree
BACCALAUREUS INGENERIAE in
ELECTRICAL AND ELECTRONIC ENGINEERING SCIENCE
at the
UNIVERSITY OF JOHANNESBURG

___________________________________
Name: M.K
Surname: Mashiane
Student Number: 220105496
Student, University of Johannesburg
Module: ETN2B
Date: 05 October 2022
Plagiarism Declaration
I, _____M.K.Mashiane____________ an Electrical and Electronic Engineering Student at the
University of Johannesburg, hereby declare that the content of this document is of my own
work. I understand what plagiarism constitutes, and that all unethical academic behaviour is
punishable by disciplinary action as deemed fit by the university.
Table of Contents

Table of Figures ............................................................................................................................................3

Aim .................................................................................................................................................................4
Literature.......................................................................................................................................................4
Experimental Setup ......................................................................................................................................6
Experimental Results ....................................................................................................................................9
Discussion ....................................................................................................................................................10
Conclusion ...................................................................................................................................................11
References ....................................................................................................................................................11

Table of Figure
Figure 2.1 measurement across whole circuit

Figure 2.2 measurement across capacitor

Figure 2.3 measurement across resistor
Figure 2.4 measure across whole circuit
Figure 2.5 measurement across inductor

Figure 2.6 measurement across resistor

Figure 1.1 wattmeter

Figure 1.2 rms power source

Figure 1.3 conducting cables(banana-banana/banana-croc//croc-croc0

Figure 1.4 a multimetre

Figure 1.5 20uF capacitor

Figure 1.6 40 resistor

Figure 1.7 0.3 H inductor

Aim
The aim is to build a series connection of a capacitor(and/or inductor) and a resistor to create an AC
load, measure the power and the current in the circuit and the voltage across the capacitor and
resistor and finally construct phasor diagrams and power triangle of the system and compare to the
results of the two circuits.

Literature
All electrical and electronic circuits contain capacitance. This report will attempt to introduce two
energy storage circuit elements, the capacitor and the inductor.

A Watt meters is a device used for measuring the power in watts of any given circuit. You can find
these power meters in residential areas for determining the energy consumption and utility frequency.
[1]

The capacitor: stores energy in an electric field. It can be constructed by using two parallel
conducting plates separated by distance d. Electric charge is stored on the plates, and a uniform
electric field exists between the conducting plates whenever the capacitor has a voltage difference
across it. The space between the plates is filled with a dielectric material ( i.e. impregnated paper,
mica sheets, ceramics, metal films, or just air). The dielectric material, called the dielectric constant,
describes the relationship between the electric field strength and the capacitor voltage. Capacitors are
measured in capacitance which is expressed as the ratio of the electric charge(Q) on each conductor to
the potential difference(V) between them. Q=CV. C=E0*A/d The SI units for capacitance is
Farads(F).

Below is a figure showing a capacitor

[3]

Figure a: a capacitor diagram

 According to [3]Capacitors are widely used in electronic circuits for blocking direct current while
allowing alternating current to pass. In analogue filter networks, they smooth the output of power
supplies. In resonant circuits they tune radios to particular frequencies,

The current through a capacitor due to an AC source reverses direction periodically. That is, the
alternating current alternately charges the plates: first in one direction and then the other. With the
exception of the instant that the current changes direction, the capacitor current is non-zero at all times
during a cycle. For this reason, it is commonly said that capacitors "pass" AC. However, at no time do
electrons actually cross between the plates, unless the dielectric breaks down. Such a situation would
involve physical damage to the capacitor and likely to the circuit involved as well.

Since the voltage across a capacitor is proportional to the integral of the current with sine waves in
AC or signal circuits this results in a phase difference of 90 degrees, the current leading the voltage
phase angle. It can be shown that the AC voltage across the capacitor is in quadrature with the
alternating current through the capacitor. That is, the voltage and current are 'out-of-phase' by a
quarter cycle. The amplitude of the voltage depends on the amplitude of the current divided by the
product of the frequency of the current with the capacitance.

The inductor: stores energy in a magnetic field. An inductor can be constructed by winding a coil of
wire around a magnetic core. The inductance of an inductor depends on its size, materials, and method
of construction. The inductance is given by the equation

[5]

The concept of inductor is widely used in electrical circuits and electronics, ranging from being used
as transformers, sensors, relays, used to tune circuit and as filters. Supposing that an inductor has no
energy stored in initially. At an initial time, t=0 a voltage will be allowed across the inductor and a
current will try to pass through it. But the inductor will oppose the change in current, this by Lenz’s
law. The current gradually increasing until its value of final current. At the same time the voltage
across the inductor will decrease unless its zero. [6]
Because inductors are made to react against the change in current, it causes it to lag behind the
voltage. When you apply a voltage to an inductor, you make a magnetic field. Henceforth, if the
magnetic field varies with respect to time, there is an electric field that opposes the magnetic field
inside the inductor. In other words, the electric field generated by the voltage behaves like a wall to
the magnetic field generated by the current.

This behavior is described by Len'z Law.

𝐸𝑀𝐹=−∂Φ𝐵/∂𝑡

, which happens to be the negative of Faraday's Law of Induction. [6]

Experimental Setup
Capacitive circuit

Build a series connection of a 20µF capacitor and a 40Ω, 40W resistor to create an AC load.

1. Measure the power and the current in the circuit.

2. Measure the voltage across the capacitor and resistor.

Note: The maximum current in the circuit should not exceed 1 A

3. Construct a phasor diagram and power triangle of the system

Inductive circuit

Build an inductive load in series with resistor and inductor can be used (The inductor used has an
iron core).

1. Measure the power and the current in the circuit.

2. Measure the voltage across the inductor and resistor. to somehow determine the linearity of the
inductor.

3.Construct a phasor diagram and power triangle of the system The components that are to be used
have nominal values of: C= 20µF; 250V,R= 40Ω , 40W and L= 0.3H, (110V winding of a 220/110V
280VA transformer)

Below is series of figures showing the components used in the practical

Figure 1.1 wattmeter

Figure 1.2 rms power source

Figure 1.3 conducting cables(banana-banana/banana-croc//croc-croc

Figure 1.4 a multimetre

Figure 1.5 20uF capacitor

Figure 1.6 40 ohms resistor

Figure 1.7 0.3 H inductor

Experimental Results
Below is series of pictures showing the results we got for the two circuit configurations

Figure 2.1 measurement across whole circuit

Figure 2.2 measurement across capacitor

Figure 2.3 measurement across resistor

Figure 2.4 measure across whole circuit

Figure 2.5 measurement across inductor

Figure 2.6 measurement across resistor

Discussion
Following the instructions and guidelines mentioned in the Experimental Setup, a series connection
of a capacitor (and/or inductor) and a resistor to create an AC load was built; to measure the power,
the current in the circuit and the voltage across the capacitor and resistor and finally to construct
phasor diagrams and power triangle of the system and compare to the results of the two circuits.
Starting with the capacitor, it was observed that voltage lags the current in RC (resiyor-capacitor0
circuit and that it leads in the inductor-resistor circuit.
Because inductors are made to react against the change in current, it causes it to lag behind the
voltage. When you apply a voltage to an inductor, you make a magnetic field. Henceforth, if the
magnetic field varies with respect to time, there is an electric field that opposes the magnetic field
inside the inductor. In other words, the electric field generated by the voltage behaves like a wall to
the magnetic field generated by the current. This behaviour is described by Len'z Law.

The current through a capacitor due to an AC source reverses direction periodically. That is, the
alternating current alternately charges the plates: first in one direction and then the other. With the
exception of the instant that the current changes direction, the capacitor current is non-zero at all times
during a cycle. For this reason, it is commonly said that capacitors "pass" AC. However, at no time do
electrons actually cross between the plates, unless the dielectric breaks down. Such a situation would
involve physical damage to the capacitor and likely to the circuit involved as well. Since the voltage
across a capacitor is proportional to the integral of the current with sine waves in AC or signal circuits
this results in a phase difference of 90 degrees, the current leading the voltage phase angle.

Conclusion
We can conclude that a capacitor an inductor and an op-amp can give functions in a circuit depending
on the way they are connected. The energy storage nature of the capacitor and the inductor creates a
phase shift in the voltage and the current, with the voltage lagging in an rc circuit and leading in an
inductor resistor circuit.

References

References

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[ “Google,” [Online]. Available: http://www.google.com/google-images-capacitor-diagram. [Accessed

2 27 September 2022].
]

[ C. Cunningham, “Adafruit,” [Online]. Available: https://learn.adafruit.com/circuit-playground-c-is-for-

3 capacitor/what-is-a-capacitor. [Accessed 27 September 2022].
]
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] 728.jpg?cb=1242001980. [Accessed 2022 September 2022].

[ “electric-shocks,” [Online]. Available: https://electric-shocks.com/rl-circuit-analysis/. [Accessed 27

5 September 2022].
]

[ “elctrocnics,” [Online]. Available: https://electronics.stackexchange.com/questions/371650/why-

6 does-current-lag-90-degrees-behind-the-voltage-when-an-inductor-is-present.
]

[
7
]

[ -Richard-C.-Dorf-James, Introduction-to-Electric-Circuits-8th-Edition, California: Elm Street Publishing

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]

[ M. &. D. K. O. a. L. C. dr. Gololoo, “ETN2B Practical Guide,” Electrical and Electronic Engineering
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]