Download Chapter 1 - Elements of Electrical Circuits: The Nuts and Bolts of

Chapter 1
- Elements of Electrical Circuits: The Nuts
and Bolts of Circuits
Electricity, or rather electrical circuits, is the blood of our modern society. We live in a world
surrounded by electrical appliances, ranging from a simple light bulb to a highly sophisticated
cell phone. We will begin our study of electrical circuits here.
The study of electrical circuits involves:
•
The understanding of how electric current arises.
•
The function of various electrical devices.
•
The design of electrical circuits to achieve certain purposes.
For now we will begin by studying the important elements in an electrical circuit, namely
electrical currents, voltage, electrical power and resistance.
The term electricity in physics is a more broad area of study of the nature of interaction
between electric charges. We will study the nature of electrical interaction in more detail later.
All that we need to know is that:
1. Charges come in 2 flavors, positive and negative. Like charges repel while unlike
charges attract. Further, the amount of charges is measured in coulombs with unit .
2. Matter around us can be broadly classified as electrical conductors and insulators.
Conductors allow electric current to flow past them easily while insulators does not
allow electric current to flow past them. We will study why this is the case later.
What are electrical circuits?
Electrical circuits are wires, which are made of electrical conductors, connected to various
components such as battery, switches and electrical devices. The reason they are called
electrical circuits is the wires must form a loop in order for current to flow.
Consider a simple electrical circuit with a battery
connected to a light bulb as shown on the right:
The battery will push electric charges around the
wire loop, resulting in a flow of positive charges
from the positive terminal to the negative terminal of
the battery.
This flow of electric charge is called an electrical
current. (This is called the conventional current flow, but in reality in metal wires, it is the
negatively charged electrons flowing in the opposite direction, but this can be ignored.) We
will quantify them shortly.
The wire in an electrical circuit form a loop for a continuous current flow, if not charges will
accumulate on its end point and prevent any more current from flowing through it.
In the process the electrical current flowing through the light bulb will cause the light bulb to
be switched on, giving off light in the process. In effect, the current carries electrical energy
that are converted from the battery and brought into the light bulb, so it can be converted into
light energy. The energy conversion cab be summarized as:
Chemical
Electrical Energy in
Light Energy given
Energy from
the electrical current
off by the light bulb
battery
This simple example is highly instructive as it illuminates some things we will have to account
for in electrical circuits, which are electrical currents and energy conversion.
Electrical Currents (or simply Current)
In order to quantify the flow rate of an electrical current,
consider a cross-sectional area of a wire with a current
flowing through it as shown on the right:
The electrical current is defined to be the amount of charge
flowing through per unit time and it is given by:
Where
is the amount of charge flowing through the cross-sectional area, while
is the time
taken. The SI unit for current is amperes denoted by ; 1 of current means that in 1 , 1 of
charge have passed through the area.
Actually it needs to be mentioned that there are two forms of current flow, direct current (DC)
and alternating current (AC). The simple battery with light bulb example earlier is an example
of a DC circuit, where current flows steadily in one direction. AC on the other hand transmits
energy by having a current that flows back and forth the circuit as shown by the following
current-time graphs:
From here on, we will be working exclusively with DC circuits as they are a lot simpler since
the current and voltage are held constant. We will study AC circuits in more detail in
Electromagnetism.
Voltage: Electromotive Force and Potential Differences
The other thing we have to account for in electrical circuits is the energy conversion. As we
have noted earlier in the simple circuit with the light bulb, there are two different energy
conversions:
1. The conversion of the stored energy in a battery into electrical energy.
2. The conversion of electrical energy into light energy by the light bulb.
These energy conversions can be generalized to the following 2 types:
1. The conversion of other forms of energy into electrical energy; this conversion is not
limited to batteries, other examples include the conversion of kinetic energy to electrical
energy by generators.
2. The conversion of electrical energy to other forms of energy; this conversion is usually
performed by electrical appliances such as light bulb, heater, speaker and so on.
To account for the amount of energy used, we will have to introduce another quantity called
voltage which is generally defined as the work done (the amount of energy converted) per unit
charge flowing through the component:
For example:
•
A typical 1.5 battery will convert 1.5 of its chemical potential energy into electrical
energy for every 1 of charge that flows through it.
•
A 9 speaker will convert 9 of electrical energy into sound (and some heat due to
inefficiencies) energy for every 1 of charge that flows through it.
Clearly there are two different forms of voltage that we should be aware of.
One is called the electromotive force or EMF for short (not a force), usually denoted by , the
voltage involved in pushing the current around the circuit. The
in the definition of voltage is
the amount of other forms of energy converted into electrical energy.
The other is potential difference (also commonly called voltage drop), usually denoted by ,
the voltage involved in draining the electrical energy from the circuit. The
in the definition
of voltage is the amount of electrical energy converted into other forms of energy.
In practice, the term voltage is used which could mean either the electromotive force or
potential difference, so it is important to have a clear understanding of the both of them and
distinguish them clearly.
Electrical Power
Consider the multiplication of current with voltage:
Based on their definitions, the multiplication of and
results in the quantity , which is the
amount of work done per unit time. In physics, this quantity is called power, which is the rate
of work done; with SI unit of watts which the rate at which 1 of work done in 1 .
Hence the electrical power is given to be:
Once again, electrical power can mean two things; either the rate of electrical energy
generation by an electrical power source or the rate at which electrical energy is drained by an
electrical device.
To determine the amount of electrical energy being consumed or generated, we will have to
multiply the power and the time that has elapsed:
Household electrical energy usage is usually measured in kilowatt-hours,
joules, . 1
ℎ rather than
ℎ of energy is equivalent to the electrical energy consumed by a 1
electrical
device for 1 hour, which is a total of 3.6 million joules of energy, which is a lot of energy! In
other words, 1
ℎ
3.6
3.6 × 10 .
Resistance: Ohmic and Non-Ohmic Devices
Going back to the example of the simple light-bulb switch. On one hand we have the battery
pushing the current, supplying electrical energy; and on the other hand we have the light-bulb
draining away electrical energy.
How does this affect the current flowing through it? Of course, the stronger the electromotive
force, the larger the current.
Another factor that affects the amount of current flowing through depends on the device as well
(its construction and its material). The less conductive the device is, the lesser the current. The
degree of conductance of a device is measured by its resistance . The higher the resistance,
the less conductive it is, making it difficult for current to flow through.
For most conductors, the amount of current flowing through it is directly proportional to the
applied electromotive force, with the constant of proportionality being
used is that for a given voltage, the larger the
!
(the reason ! is being
value, the lower the current is, reflecting the
nature of electrical resistance):
Such conductors are called ohmic conductors, where if a graph of applied voltage
and current
flowing through it is plotted, it will result in a straight line through the origin. The gradient is
then ! as shown:
Non-ohmic conductors on the other hand, have a non-linear
graph, so it does not have a
well-defined resistance. Nonetheless, non-ohmic conductors are also important in practice,
such as diodes.
graphs are called characteristic graphs as it highlights how is current flowing through the
device based on the voltage applied to it, displaying its electrical characteristic. The following
sketch contrast their
characteristics:
To find , we can rearrange the equation
"
!
to obtain the following formula to calculate
resistance as a ratio to the voltage applied and the current flowing through it:
Using this formula, we can measure a device’s resistance, which can be used to predict the
amount of current flowing through it for any given applied voltage (assume any device is
ohmic unless told otherwise). The unit of resistance is ohms, denoted by Ω.
Finally by rearranging the equation
"
$
, the potential difference of the electrical device can
be found by knowing its resistance and the current flowing through it by
. This equation
will be used often when we cover and apply Kirchhoff’s law later.
To calculate the power consumed by a device given its resistance, the following equations can
be used (which can be shown easily by combining the equation
%
%
and
"
$
):
It is important to note that
in these equations are the potential difference across the electrical
device, not the electromotive force of the connected battery. It is implicitly assumed that the
potential difference is equal to the electromotive force when a single device is connected to one
single battery. We will see why this is the case when we look at Kirchhoff’s law later.
Any devices that has a resistance to them are called resistors. Their function in the circuits are
mainly, but not restricted, to restrict the amount of current flowing and draining away electrical
energy.
The electrical energy converted can either be useful such as heat (a heater is just a giant
resistor) and light, or waste energy to be dumped into the surroundings.