DC Electricity

Notes are supplements, not substitutes for books!

There are several different branches of electricity but fortunately or unfortunately we’ll be dealing with just DC
electricity for our AS syllabus. DC is short for direct current which means current flows in one direction only.
While dealing with electricity you should have an in-depth idea about the following basic terms – current,
voltage and resistance. Let’s start with voltage.

Voltage is what drives the current in the circuit. Question is….HOW. This actually gives rise to a second
question – what is current. Current is the rate of flow charge. Needless to mention, electrons are the charge
carriers. So going back to the first question, the voltage provides the energy to the charges enabling them to
flow in the circuit. That’s why voltage is at times referred to as the energy per unit charge. At this point a
simple circuit would help to describe voltage in details. Take a look at the diagram below –

The diagram shows a light bulb connected to a cell. The cell

provides the total electrical energy for charges to flow in the
circuit. This is called emf, short for electromotive force. And
the voltage drop across the bulb is called the potential
difference. This will be described in details in later sections
but for the time being just remember that voltage has two
subcategories – emf and pd.

It should be clear by now that current only flows in the

circuit when you provide a voltage. Now you should be capable of identifying the dependent and independent
quantity among current and voltage in a circuit. Now is as good a time as any to learn some of the technical
terms regarding electrical circuitry. Just remember the two phrases – current through and voltage across.
Speaking of current and voltage, there’s a relationship between them that you must be acquainted with. Mr Ohm
was the first guy to establish the relationship between these two quantities and named it Ohm’s law.
Ohm’s law states that the current through a conductor is directly proportional to the voltage across it
provided that all other physical factors (basically temperature) remain constant. Take a look at the following
graphs –

You should know by now what the graph of directly proportional quantities look like. So it should be obvious
that the first graph is for an ohmic conductor (a conductor that obeys Ohm’s law). How would you describe the
second graph? For the time being just know that it’s a non ohmic conductor. Coming back to the graph, what
will the first graph look like if the axes are reversed? THE SAME! However if you reverse the axes and then
find the gradient of the graph, the quantity you will get is the resistance. This is best explained by the equation
relating voltage, current and resistance, V = IR
From the equation, for voltage and current to be proportional to each other, the resistance must remain constant. Now if
you look at the second graph, its not hard to tell that it’s not a straight line graph which means that in this scenario the
current is not proportional to the voltage. This is because now the resistance changes. Why and how the resistance
changes will be discussed in later sections.
We have learned enough about voltage. Now let’s take a deeper look into current. By definition current is the rate of flow
of charge. Mathematically I = Q/t
So if you think about it current is basically the flow of electrons but in the opposite direction. This is called conventional
current whish assumes current always flows from the positive terminal to the negative terminal of a cell.
Even though the definition/equation of current is simple, it is insufficient for fully analyzing the factors affecting the flow
of current through a conductor. That’s where the transport equation comes in handy.

I = nAve , where I is the current through the conductor, n is the charge carrier density, A is the cross sectional area of the
conductor, v is the drift velocity and e is the charge of an electron.

n is the number of electrons (charge carriers) per unit volume. That’s why it’s called charge carrier density. Under
normal circumstances, n remains the same but for materials that have a negative temperature coefficient (NTC) of
resistance, n increases with temperature. If you’re thinking what NTC is, just rearrange and read the previous line. You
should get your answer. And if you are wondering how this happens just remember the following lines in the correct order.
As the material gets hotter, increased vibration of the atoms releases more electrons which basically increases the charge
carrier density, n

v is the average velocity that a charge carrier(electron) attains while traveling through a conductor. What you really need
to remember is the effect of temperature on v. The drift velocity decreases when the temperature of the conductor
increases. Question is how? As electrons move through the metal, they collide with vibrating atoms of the metal. As the
temperature rises, the atoms vibrate more vigorously. There are more collisions between the atoms and the electrons
which basically slows them down. i.e. their drift velocity decreases.

Now is a good time to apply the transport equation to analyze some of the graphs. Take a look at the second graph in the
last page. This is basically the generic V-I graph of metals for example, a tungsten filament inside light bulbs. There are
free electrons in metals.
As electrons move through the metal they collide with the atoms which are already in vibration. Current in the
wire produces heating effect which causes a greater collision between the electrons and the atoms of the metal. This
decreases the drift speed. According to the equation I = nAve, if v decreases the current decreases. A decrease in
current means the resistance had increased.
Can you figure out the steps how the resistance changes with temperature for semiconductors e.g. NTC thermistors. I’ll
save you the trouble –
Current produces a heating effect. As the temperature rises, increased vibration of the atoms releases free
electrons which effectively increase the charge carrier density, n. According to the transport equation, as n
increases, the current increases. An increase in current means the resistance has decreased.
Let’s take a look at some of main the symbols for electrical devices.

Circuit Components
Voltmeters measure the voltage across a component and should therefore always be connected in parallel. Voltmeters
have a very high resistance so that almost no current can flow through it and lost volts is nearly zero. If a voltmeter is
connected in series with a component, no current will flow through it and since its resistance is very high, the maximum
voltage drop would be across the voltmeter.
Ammeters measure the current through a component. Since current remains constant in series, ammeters should therefore
always be connected in series. Ammeters have negligible resistance so that there is no voltage drop across it. An ammeter
with a resistance will reduce the current being measured. If however, (by mistake) an ammeter is connected in parallel
with a component, all the current will flow through it creating a short circuit and the component will not be powered.
 CIRCUITRY

Obviously you won’t need all the symbols for our syllabus. I guess you are already aware of the different
symbols but now lets take a while analyzing the patterns. Any component with an arrow sign through it is
variable. For instance look at the symbol for the variable resistor. Similarly if you had a power supply with an
arrow through it, it would have been a variable power supply. Likewise arrows falling on a component imply
that it’s light dependent. Now let’s construct some circuits using these components. But before that you need to
have these ideas on top of your head at all times.

When two components are connected end to end with no other junctions between them, they are said to be
connected in series. In simpler terms if two components have only one connecting wire between them they are
in series. Similarly if two components are connected with two connecting wires, they are said to be in parallel.
To create a bridge between the two concepts you need to recall the behaviour of current. Current always
branches out (gets divided) at the junctions. Since series circuits don’t have any junctions, the current in a series
circuit remains the same. On the other hand, parallel circuits are associated with branches. Which means
that current gets divided (shared among components) in parallel. Voltage behaves exactly the opposite way of
current – remains the same for components in parallel and gets shared among components in series. Take a look
at the diagrams below:

For the time being, consider that all the resistors are identical. If the emf of the cell is ..say 6V, what will be the
readings on the ammeters and voltmeters shown in the diagrams? First consider the series circuit. We know that
in a series circuit the current remains the same. So if we had placed an ammeter between the two resistors or
after the second one, in either case, the ammeter reading would have been the same.
However, since the voltage gets shared and the resistors are identical, the voltage will be divided equally among
the two voltmeters and the voltmeters will read 3V apiece.
Now for the parallel circuit the voltmeter will read 6V as the voltage remains the same in a parallel circuit.
However A1 will give the total circuit current but as the current enters the parallel branch, it is divided and since
the resistors are identical, the current is divided into two equal parts. If there were three identical resistors, the
current would have been divided into three equal parts. Now let’s deal with the resistance.
Always remember the total resistance in a series circuit is the sum of the individual resistances.
Rtotal = R1 + R2
The total resistance in a parallel circuit is the inverse of the summation of the reciprocals of the individual
resistances. It sounds confusing but the formula isn’t that clumsy as the description in words.

Now what if the resistors were not identical. What difference would that make? Well if the resistors are
connected in series, irrespective of whether they are identical or non identical, the current will be the same at
any given point. However if non identical resistors are connected in series the voltage divided across them
depends on resistance – the greater the resistance, the larger is the voltage drop across it.
Take a look at the diagram below.

Since the resistors are non identical now, how do you think the voltage will be shared? Since the allocation of
voltage in a series circuit solely depends on the resistance, a formula relating them will be helpful at this point
V1/V2=R1/R2. Needless to mention, you need three of the four quantities to be able to use this equation. However
it’s obvious from the diagram that the ratio of the two voltages across the two resistors will be 1:2. What if one
of the resistors is variable; let’s say a thermistor as shown below.

What happens to the voltmeter reading when the

temperature of the thermistor increases? First recall
what happens to the resistance of a thermistor when its
temperature rises. The resistance of a thermistor
decreases with temperature. Now what do we know
about voltage in a series circuit? The total voltage is
shared among the components. Therefore the total
voltage always remains the same but as the resistance
of the thermistor decreases, the voltage across it
decreases. As the total voltage remains constant, the voltage across the resistor will increase, effectively
increasing the voltmeter reading. Try figuring out what will happen to the voltmeter reading if the temperature
of the thermistor decreases. Also try to figure out what will happen if the thermistor is replaced with an LDR
and the light intensity is varied.
Now that you know now more or less about resistors and voltages in circuits, let’s take a look at an advanced
concept – potential divider. As the name suggests, the potential difference (voltage) is divided in a potential
divider. However there are a few fancy names for potential divider – rheostat and potentiometer. Collectively
they can all be considered to be variable resistors. Now that you have the basic idea about variable resistors, its
time you know the categorization as well. A variable resistor is called a rheostat. It can be either used to vary
the potential difference or the resistance.
Look at the diagram below. The device is called rheostat. Diagram a is the circuit used to vary the resistance
while b is used to vary the potential difference.
 Application of potential divider

The diagram on the left shows two resistors

connected in series. By this time it should be
pretty obvious that the total voltage VT will be
shared among the two components, R1 and R2.
Question is in what proportion? It has already
been discussed that the voltage gets shared
according to the ratio of the resistances.
Therefore

Now take a look at the diagram on the left. This

is an actual potential divider. Can you figure out
the difference between the two setups? Even
though they look different, their working
principles are quite the same. Just consider the
rings of the rheostat to be resistors connected in
series with one another and you should be able
to grasp the entire idea. Try to figure out from
the diagram at which point will the voltmeter
show the maximum and minimum reading.

Since we have taken our time to delve into details about resistors, let’s shed some light on the basics of
resistance. Resistance of a material is depends on three factors – its length, area and resistivity. Resistivity is the
property of a material. For instance the resistivity of a copper wire of length 1m and diameter 1mm will be same
as any other length and diameter of the wire, provided that it’s COPPER.
They are linked by the equation –

Where,
ρ is the resistivity
is the length and
is the cross sectional area of the material

That being said, go to the previous section and try to figure out how moving the slider changes the resistance. HINT:
Internal Resistance
The resistance inside a power supply is called its internal resistance. The term internal should suffice to convey
the idea that the source itself imparts the resistance.

Figure 1 Figure 2

Figure 1 shows a regular cell connected to a load resistor R. You could expect that the emf of the cell to be
equal to the potential difference across the load resistor R, since there are no other components in the circuit.
Figure 2 on the other hand will clear up the misconception. Figure 2 shows there is an internal resistance inside
the cell. What can you deduce about the circuit in figure 2? The load resistance and the internal resistance are
basically in series. that’s why the total voltage (emf) is shared among the two components. Mathematically
E.m.f = Vload resistor + Vinternal resistor. Since the current through both the resistors is constant, The equation can be
rewritten in terms of I, R and r because VR = IR and Vr =Ir.
E.m.f = IR + Ir
However if you wish to find the r using a graphical method, you need a circuit like the one shown below.
Current and voltage are recorded for different settings of the rheostat and a graph of V vs I is drawn.

The negative of the gradient of the graph gives the internal resistance
&
The y-intercept gives the emf of the power source
POWER
The power dissipation in a resistor is the product of the voltage across it and the current through it, P = VI.
Since V = IR and I = V/R substituting the values of V and I in the first equation will give two more equations
of power – P = V2/R and P = I2R

If you analyze the generic definition of power, it is the rate of transfer of energy. In this context it is the rate of
transfer of electrical energy. So P = E/t. Rearranging the equation E = Pt and since P = VI, E = VIt
Those being said, try to figure out the power dissipation changes in the load resistor for the circuit above.
Power will at times also be referred to as the rate of energy transferred.

Some important graphs associated with electricity (Look at the axes carefully)
 Ask Yourself

● What will be the voltmeter reading if the open ends of a cell are connected to a voltmeter?
● Two pieces of wire of same length, one with a diameter twice than the other are connected end to end. What
will be the current through the thicker wire?
● For the same two wires in the previous question, what will be the resistance of the thinner wire compared to
the thicker one?
● What about the drift velocity in each wire?
● What is a non S.I unit of voltage? Please don’t think of mV, kV or MV.
● What equation should you use to find the kinetic energy of an electron of charge e, accelerated through a
potential difference of V?
● What will be the shape of the graph of Power against Voltage for an Ohmic conductor?
● What is terminal P.D? If it’s the pd across a cell, why is this not equal to the emf?
● What will be the shape of Resistance against Potential Difference graph for a filament lamp
● How would you find the resistance from a V-I graph for a non Ohmic conductor? (Not a straight line)
● In what orientation are the ports of a multiplug arranged – series or parallel? Give a reason for your answer
● What happens when you connect two non identical batteries (with internal resistance) in parallel?
● What happens when you connect the same two batteries in series?
● What happens to the total resistance of a parallel combination if one of the resistances decrease?
● What is the shape of the graph for current against resistance for constant voltage? How would you construct a
circuit for this purpose?
● WA-2 is a non SI unit for a quantity. What is it?
● What will be the shape of the graph for power against resistance for a load resistor?
● How does the power dissipation change for components in series and parallel?
● Why is the energy of a battery expressed in Ampere-hour?
● What happens if you connect a voltmeter in series with a resistor in a circuit?