BIOMEDICAL ENGINEERING TECHNOLOGY
(Fundamentals of Electric al & Electronic s I)
© Kalupa C S, 2019
Fundamental Principles of Electricity
Introduction
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Electricity may be defined as the flow of electrons in a material
A random movement of conduction electrons in a material does not necessarily constitute a flow of
an electric current.
An electric current flows when the conduction electrons drift in a specific direction within a particular
material.
For the electric current to continue flowing the conductor must be in a continuous loop called an
electric circuit.
A force is also required to keep the electrons moving round the circuit.
Electric Current (I)
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This is the quantity of electricity that passes a given point of a circuit in a given period of time. It is
the rate at which electric charge (Q) is moved around the circuit.
If Q is the amount of charge going past a point in a period of time t, then
𝐼 = 𝑄⁄𝑡
The unit of charge is the coulomb (C). Thus, when one (1 C) coulomb of charge flows past a point in
one second (1s), we have
𝐼 = 1𝐶⁄1𝑠 = 1 𝐶⁄𝑠 = 1𝐴
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Note that the SI unit of an electric current is the ampere (A). One ampere is said to flow past a point
when one coulomb of charge goes past that point in one second.
Electromotive force (e.m.f)
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For conduction electrons to continue moving around the circuit, a force is required to help them to
overcome obstacles in their path.
Electromotive force (e.m.f) is the total driving force for the conduction electrons. The unit of e.m.f is
the volt (V).
Resistance
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When electrons flow through a conductor, they face obstacles as they negotiate their way through
the complex molecular structure. This leads us to defining a material property called resistance.
Resistance is the opposition to the flow current in a purely resistive material. The unit of
resistance is the ohm (Ω).
Resistor
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A resistor is a dissipative element that converts electrical energy into heat energy. Its value depends
on the type and shape of the resistor material.
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BIOMEDICAL ENGINEERING TECHNOLOGY
(Fundamentals of Electric al & Electronic s I)
© Kalupa C S, 2019
Potential Difference (p.d.)
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The potential difference (p.d.) is the difference in voltage levels between two points in a circuit. It is
measured in volts (V).
Potential difference (p.d.) is related to the current flowing through a resistor. It is very different from
e.m.f, the driving force that keeps electrons moving in a circuit.
Whenever current flows through a resistor, there will be a p.d . developed across the resistor.
Note that e.m.f causes a p.d. across any two points in a circuit.
Ohm’s Law
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A voltage source V, connected across a resistor R, will cause a current I to flow through the resistor.
Within a certain temperature range, the applied voltage V is directly proportional to the current flow
I.
𝑉∝𝐼
∴ 𝑉 = 𝑘𝐼
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The constant of proportionality k = R, the resistance of the material. Thus, 𝑉 = 𝐼𝑅, which is Ohm’s
law.
Examples
1) A current of 5.5 mA flows through a 33 kΩ resistor. Calculate the p.d. thus developed across it.
2) If a p.d. of 24 V exists across a 15Ω resistor then what must be the current flowing through it?
Conventional current and electron flow
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The direction of current flow in electric circuits is from the positive plate of the battery, through the
circuit, returning to the negative battery plate. This is called conventional current flow.
However, electrons are negatively charged particles, which move from the negative plate to the
positive (the electron flow) or the true direction of current flow.
It so happens that before science was sufficiently advanced to have deeper knowledge of the
electron; it was assumed that the positive plate represented the ‘high’ potential and the negative the
‘low’ potential. So the convention was adopted that the current flowed around the circuit from the
high potential to the low potential.
Resistivity
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The resistivity (𝜌) is the basic property that indicates the material’s capability to resist a current flow.
The resistance (R) of a uniform cross-section material, such as a wire, depends on the length (L),
the cross sectional area (A) and the resistivity (𝜌) so that
𝑅 = 𝜌 𝐿⁄𝐴
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The unit of resistivity is the Ohm – metre (Ω-m). Note that is different from resistance measured in
ohms (Ω).
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BIOMEDICAL ENGINEERING TECHNOLOGY
(Fundamentals of Electric al & Electronic s I)
© Kalupa C S, 2019
Conductivity
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It is much more convenient to consider the material’s ability to conduct electricity rather than resisting
current flow. In view of this, we define the materials capability to conduct electricity as the electrical
conductivity 𝜎 ;
1
𝜎=
𝜌
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The unit of electrical conductivity is per Ohm-metre (Ω𝑚)−1 .
Conductance
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Conductance is related to the resistance. It is not the same as the conductivity!
Resistance is the opposition to current flow, but conductance of a conductor is the inducement to
current flow.
If R is the resistance of a conductor, its conductance G is given by
𝐺=
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1
𝑅
The SI unit of conductance is mho (i.e., ohm spelt backward).
It is a usual practice to use Siemen as the unit of conductance, denoted by the symbol S .
Examples
1) A wire-wound resistor is made from a 250 metre length of copper wire having a circular cross -section
of diameter 0.5 mm. Given that the wire has a resistivity of 0.018 µΩ m, calculate its resistance
value.
2) The resistivity of hard drawn Aluminium at 200C is 28µΩ-mm. What is the voltage drop per unit
length of a 4mm diameter wire carrying a current of 5A? Hint [V = IR].
3) Calculate the
i)
Resistance of 100 m of copper cable of 1.5 mm 2 cross-sectional area if the resistivity
of copper is taken as 17.5 x 10-9 Ω m.
ii)
Resistance of 100 m of aluminium cable of 1.5 mm 2 cross-sectional area if the
resistivity of aluminium is taken as 28.5 x 10 -9 Ω m.
Note
The above examples show that the resistance of an aluminium cable is some 60% greater than a copper
conductor of the same length and cross-section. Therefore, if an aluminium cable is to replace a copper
cable, the conductor size must be increased to carry the rated current.
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BIOMEDICAL ENGINEERING TECHNOLOGY
(Fundamentals of Electric al & Electronic s I)
© Kalupa C S, 2019
Effect of Temperature on Resistance
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The resistance of a material also depends on its temperature and has a property known as its
temperature coefficient of resistance.
The resistance of all pure metals increases with increase of temperature. The resistance of carbon,
insulators, semiconductors and electrolytes decreases with increase of temperature. For these
reasons, conductors (metals) are said to have a positive temperature coefficient (PTC) of resistance.
Insulators etc. are said to have a negative temperature coefficient (NTC) of resistance.
Temperature coefficient of resistance is defined as the ratio of the change of resistance per degree
change of temperature, to the resistance at some specified temperature.
The temperature coefficient (α) is usually specified at 0 0C and the resistance of the material at this
temperature is denoted by Ro.
Temperature coefficient of resistance is defined as the ratio of the change of resistance per degree
change of temperature, to the resistance at some specified temperature. The quantity symbol is α
and the unit of per degree Celsius.
If a conductor has a resistance R0, R1 and R2 at 0 oC, t1 oC and t2 oC respectively, then
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The average rise in temperature will be (t2 − t1)°C.
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Questions
1) The coil of an electric motor has a resistance of 250Ω at 20 oC. Calculate the resistance of the coil
if the motor temperature increase by 45 oC. Assume α = 0.00425/ oC, referred to 0 oC.
2) A carbon resistor has a resistance of 120 Ω at a room temperature of 16 oC. When the resistor is
connected in some circuit, the current flowing through it causes the temperature to rise to 32 oC. If
the temperature coefficient of carbon is 0.00048/ oC, compute the resistance under these operating
conditions.
3) A coil has a resistance of 18 Ω when its mean temperature is 20°C and of 20 Ω when its mean
temperature is 50°C. Find its mean temperature rise when its resistance is 21 Ω and the surrounding
temperature is 15°C.
4) The resistance of a transformer winding is 460 Ω at room temperature of 25oC. When the transformer
is running and the final temperature is reached, the resistance of the winding increases to 520 Ω.
Find the average temperature rise of winding, assuming that α(20oC) = 1/250 per oC.
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BIOMEDICAL ENGINEERING TECHNOLOGY
(Fundamentals of Electric al & Electronic s I)
© Kalupa C S, 2019
Resistor Colour Coding
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Colour bands are used to code the resistance of some resistors.
The code can be explained for 4 Band, 5 band and 6 band resistors as shown in figure 1.
For the four band resistor, the first three bands are used to specify the nominal value of the
resistance. The fourth band gives the tolerance.
For the 5 band and 6 band resistors, the first 4 digits give the nominal value of resistance.
Fig. 1.1: Resistor colour coding
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Note that for tolerance values, we have: Nothing = 20%, Silver = 10%, and Gold = 5%. You may wish
to make sense out of this: Big Boys Raped Our Young Girls But Violet Gave in Willingly to
George, Simon and Nathan,
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BIOMEDICAL ENGINEERING TECHNOLOGY
(Fundamentals of Electric al & Electronic s I)
Fig. 1.2: Resistor colour coding
Example
Determining the resistance of a 6 band resistor:
Fig. 1.3: 6 Band Resistor
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© Kalupa C S, 2019
BIOMEDICAL ENGINEERING TECHNOLOGY
(Fundamentals of Electric al & Electronic s I)
© Kalupa C S, 2019
Types of Resistors
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Resistors are either fixed or variable.
1) The tolerance of a resistor is the amount that its resistance can vary and still be
acceptable.
2) Resistors are either carbon composition, wire wound, or film.
3) Carbon composition resistors are the most commonly used resistors.
4) Wire wound resistors are used in high current circuits that must dissipate large amounts of
heat.
5) Film resistors offer small size with high accuracy.
6) Variable resistors used to control voltage are called potentiometers.
7) Variable resistors used to control current are called rheostats.
Electrical Energy
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Energy is simply the ability to do work
The unit of energy is the Joule (J)
Energy is closely related to Power. We define Power as follows:
Power
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Power is the rate at which work is done. Rate brings in the aspect of time.
If energy is the ability to do work, then:
𝑃𝑜𝑤𝑒𝑟 =
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𝐸𝑛𝑒𝑟𝑔𝑦 𝐽𝑜𝑢𝑙𝑒𝑠
(
⁄𝑠𝑒𝑐𝑜𝑛𝑑 )
𝑇𝑖𝑚𝑒
Note that power is simply the rate at which energy is converted from one form to another.
In electric circuits, the moving electrons (electric current) through a purely resistive material, collides
with obstacles in the path and due to friction, their kinetic energy is co nverted to heat energy.
Power dissipated in a pure resistor is given by:
𝑉2
2
𝑃 = 𝐼𝑉 = 𝐼 𝑅 =
𝑅
𝐽𝑜𝑢𝑙𝑒𝑠
The unit of power (
⁄𝑠𝑒𝑐𝑜𝑛𝑑 ) is also known as watt (W). We see that power and energy are
related as follows:
𝐸𝑛𝑒𝑟𝑔𝑦 = 𝑃𝑜𝑤𝑒𝑟 ∗ 𝑇𝑖𝑚𝑒
1 𝐽𝑜𝑢𝑙𝑒 = (1 𝑤𝑎𝑡𝑡) ∗ (1 𝑠𝑒𝑐𝑜𝑛𝑑 ) = 1 𝑤𝑎𝑡𝑡 − 𝑠𝑒𝑐𝑜𝑛𝑑
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For domestic and industrial consumption purposes, power is mostly measured in kilowatts and the
time in hours. It follows then;
𝐸𝑛𝑒𝑟𝑔𝑦 = 𝑘𝑖𝑙𝑜𝑤𝑎𝑡𝑡𝑠 ∗ ℎ𝑜𝑢𝑟𝑠
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BIOMEDICAL ENGINEERING TECHNOLOGY

(Fundamentals of Electric al & Electronic s I)
© Kalupa C S, 2019
This leads us to a commercial unit of power; the kilowatt-hour (kWh).
1 𝑘𝑊ℎ =
𝑤𝑎𝑡𝑡 𝑠𝑒𝑐𝑜𝑛𝑑𝑠
𝐽𝑜𝑢𝑙𝑒𝑠
=
1000 ∗ 60 ∗ 60 1000 ∗ 3600
Question
A small business operates three pieces of equipment for 8 hours continuously per day for five days in a week.
If the three equipment consume 10kW, 2.5kW and 600W respectively, compute the firm’s weekly power cost
if the power utility company charges 15 ngwee per unit.
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