The simplest and very basic of all laws in electrical engineering, is indeed
Ohm’s law
as it deals in the relationship between two very basic electrical
quantities namely, voltage and current in an ideal conductor. This
simple, easiest to remember 3 character law is astonishingly the
godfather of electrical engineering as all major analysis of electrical
quantities related to power, efficiency and impedance calculations of
any system is done or rather simplified using Ohm’s law.
Statement of ohm’ law
The statement of ohm’s law is simple and it says that, whenever a
potential difference or voltage is applied across a closed circuit, then
current flows through it. This current flow is directly proportional to
the voltage applied, if temperature and all other factors remain
constant. Thus we can mathematically express it as,
V ∝ I
Now putting the constant of proportionality we get,
V = IR.
This particular equation essentially present the statement for ohm’s law
where where I is the current through the conductor in units of amperes,
when the potential difference V is applied across the conductor in
units of volts, and Rin Ohm’s is the resistance of the conductor.
It’s important to note, that the resistance R, is the property of the
conductor and theoretically it has no dependence on the voltage applied,
or on the flow of current. The value of R changes only if the property
(like temperature, diameter, length etc.) of the material undergoes
modification by any means.
History of ohm’s law
In the month of May 1827, Georg Simon Ohm published a book by the
name ‘Die galvanischeKette, mathematischbearbeitet’ meaning The galvanic
circuit investigated mathematically where he presented the relationship
between electromotive force (EMF or V), current(I), and resistance
based on his experimental data.
His experiment contained the basic components of an electrochemical cell, as shown in the figure below.
1. Electrodes (X and Y) that are made of electrically conductor material like copper.
2. Reference electrodes (A, B, C) that are in electrolytic contact with an electrolyte.
3. The cell itself in a container that is made of non-reactive material like glass.
4. An electrolyte that is the solution containing ions.
Based on the results of his experiments, Georg Simon Ohm was able to
define the fundamental relationship between voltage, current, and
resistance of the circuit, which later went on to be named as Ohm’s law
and won him the Copley Medal award in the year 1841 for his excellence
in the field of science and academics. And in 1872 the term ‘OHM’ was
tagged as the unit of electrical resestance in honour of the great
scientist.
Ohm’s law physics
To understand the physics behind ohm’s in the most simplistic manner
possible let us have a look at this picture below and study it very
closely.
Ohm’s Law
From here we can draw the analogy that the person at the extreme left
is the cause or the external force due to which current (or the person
in the middle) tends to flows across a particular circuit from one end
to the other in the direction of the applied voltage. Where as the one
at the top is resistance, as it increases the difficulty for the cause
to be fulfilled, in achieving end result. The more powerful the person
at the top is, or greater the resistance, more difficulty will be
encountered by the current to flow through as a result we will get
lesser the amount than expected. Or for the flow of required amount of
current in presence of resistance, greater applied force or voltage
needs to be applied. Thus from here we can reach the conclusion that the
resistance, which is an inherent property of the conducting material,
is an independent parameter. And depending on it are the voltage and
current, which are directly and inversely proportional to it
respectively.
This is the exact phenomena that occurs even at the molecular level,
where the solid conductor is composed of free electrons as charge
carriers and also some passive elements in terms of current flow like
the ions and atoms. The atoms and ions are heavier in weight compared to
the electrons and therefore have no contribution towards flow of
current. In fact theyare the barriers, to the path of the electron flow
and is the real cause behind the resistance in a circuit. Let us look
into it in details.
When we apply a voltageV, between the leads of a resistor from an
electrical cell we can expect a current, I = V/R to flow through it. The
way the electrons move through the solid material is a bit like the way
toothpaste squeezes along a tube or as shown in the comic picture
above. The electrons keep being accelerated by the applied electric
field or voltage. This means they acquire some kinetic energy as they
move towards the +ve end of the piece of material. However, before they
get very far they collide with an atom or ion and lose some of their
kinetic energy. This keeps happening. As a result they tend to ‘drift’
towards the +ve end, bouncing around from atom to atom on the way. This
is illustrated in figure below.
This process of drifting or diffusing of electrons in the presence of
static atom is the exact reason as to why the material encounters
resistance to the flow of current and thus explains the physics behind
Ohm’s Law. The average drift velocityof the electrons is proportional to
the applied electric field. Hence the current we get is also
proportional to the applied voltage. It thus explains why we need to
constantly supply the energy to maintain the current. The electrons need
to be given the required kinetic energy to move them along, as it keeps
being ‘lost’ every time they interact with an atom. Now From law of
conservation of energy we know, that the energy of electrons lost due to
collision is not vanished or evaporated for ever, in fact it is taken
up by the atoms, as it makes them jiggle around and vibrate more
furiously due to increased energy level. Thus increasing the total
internal energy of the material and resulting in heat formation. As a
result, we see here that electrical energy is being converted into heat
energy and dissipated as loss.
The rate of energy loss or the power dissipation ,P, in the resistor
can be calculated from the equationP= VI. This equation makes sense
since we can expect a higher voltage to make the electrons speed up more
swiftly, hence they have more energy to lose when they strike an atom.
Doubling the voltage would double the rate at which each electron picks
up kinetic energy and loses it again by banging into the atoms.
The current we get at any particular voltage depends upon the number of
free electrons that are, able to flow across in response to the applied
field. Twice the number of electrons would give us twice the current.
Soit means twice as many electrons requiring kinetic energy to move them
and colliding with atoms. So, the rate at which the resistor ‘eats up’
electrical energy and converts it into heat is proportional to the
voltage and the current. i.e. the power dissipation (rate of energy
loss) is P = VI.
Applications of ohm’s law.
The applications of ohm’s law are that, it helps us in determining
either of voltage, current or resistance of a linear circuit, when the
other two quantities are known to us.
Apart from that, it makes Power calculation a lot more simpler, like
when we know the value of the resistance for a particular circuit we
need not know both the current and the voltage to calculate the power
dissipation since P = VI. Rather we can use Ohm’s Law
V = IR
Or I = V/R
to replace either the voltage or current in the above expression to produce the result
Thus, P = VI = V
2/R = I
2R. [sub V = IR]
These are the applications of ohm’s law as we can see from the results,
that the rate of energy loss varies with the square of the voltage or
current. When we double the voltage applied to a circuit obeying ohm’s
law the rate at which energy is supplied (or power) gets four times
bigger. This phenomena occurs because increasing the voltage also makes
the current rise by the same amount as it has been explained above.
Limitation of Ohm’s law
The limitations of ohm’s law are explained as under,
1) This law cannot be applied for unilateral network.
The network consisting of unilateral element like, diode, transistor
etc, which do not have same voltage current relation for both direction
of current
2) Ohm’s law also not applicable for non – linear elements.
Non – linear elements are those which do not give current through ii, is
not exactly proportional to the voltage applied, that means resistance
value of those element changes for different values of voltage and
current. Examples of non – linear elements are thyristors, electric arc
etc.
