Series Circuits

The following 3 lamps are connected "in series".

We describe these 3 lamps as being connected "in series" because:
the same current has to pass through each lamp in the circuit;
the current has no choice;
there is only one path for it to take.

The use of the word "series" here is the same as its use in "TV Series"; in other words - if you set about watching a TV Series you know that you have to watch Episode 1 then Episode 2, then 3 until you reach the end. The same is true with current flowing in a "series circuit"; it has to flow through each component in sequence until it reaches the end of the "series of components", arriving back at the p.d supply.

Now that you know what we mean by "series circuit", what is special about them?

For components connected in series:
1) there is the same current through each component (which we have already said).
2) the total potential difference of the power supply is shared between the components.
3) the total resistance of two components is the sum of the resistance of each component.

The first point has already been covered, but we need to explain 2) and 3).

2) This statement is very simple. Consider a 5V battery connected across 2 components in series:

If we use a voltmeter to measure the p.d across the lamp and discover that it is 3V, then according to the statement, we know that the p.d across the other component, the resistor, MUST be 2V because the two components share the 5V between them. (Take note: the p.d does NOT have to be shared "equally".)

A more general way to illustrate the statement is:

Now let's look at the third statement:
3) the total resistance of two components is the sum of the resistance of each component.

This is another very simple relationship, but this time it is concerned with Resistance.

Two resistors in series act like one resistor whose value is the sum of the individual resistances. As illustrated below:

Parallel Circuits

The following 2 lamps are connected "in parallel".

The word "parallel" is used because, as you can see, the lines of the paths through which the current flows are parallel to each other.

For components connected in parallel:
1) the potential difference across each component is the same.
2) the total current through the whole circuit is the sum of the currents through the parallel paths.
3) the total resistance of two resistors is less than the resistance of the smallest individual resistor.

Let's look at each of these points one at a time:
First Point: the potential difference across each component is the same.

If you built the circuit above and connected a voltmeter across the top lamp, as shown below, but then slid the left side voltmeter connector further to the left and the right side voltmeter connector further to the right (as indicated by the yellow arrows) and kept sliding them, you would find that you were effectively measuring the p.d across the power source, which in this case is 5V.

If you then connected your voltmeter across the lower lamp, as shown below, and once again slid your probes around, you would, once again, find that you were measuring the same p.d, across the power source.

So, when components are connected in parallel, the p.d across each is the same! Simple as that.

Quick Question Point 1:
Two lamps are connected in parallel; the p.d across one of them is measured and found to be 4V. What is the p.d across the other? Check

Second Point: the total current through the whole circuit is the sum of the currents through the parallel paths.

This is a really simple and obvious point. Consider the following circuit which shows currents I₁ and I₂, each of 0.5A, flowing down the paths through the lamps.
The question is: what is the current at the junction marked by the red dot and by I_T ? (where I_T stands for "total" current)

Surely I_T must be equal to 0.5 A plus 0.5 A;
so, in this case, I_T = 1.0 A

Using the letters we can write an equation:

Another way of stating the above equation, in words, is:
"Whatever current exits a junction must enter it"

So, in our example, if a total of 1.0A exits the junction, then 1.0A must have entered it.

Similarly, on the other side of the lamps there is another junction:

so whatever current enters this junction ( 0.5 A + 0.5 A) must exit it (I_T = 1.0 A), which you can see in the diagram above.

Quick Question Point 2:
A current flows from a power source and splits at a junction into two parallel paths; 1.2 A flows down one path, whilst 1.6 A flows down the other path. What current has flowed from the power source? Check

Third Point: the total resistance of two resistors in parallel is less than the resistance of the smallest individual resistor.

Once again, like point 2, this is really obvious!

Consider a circuit with just ONE resistor, say 10 Ω.

If another resistor is added in parallel, as shown below, then straight away there is an EXTRA PATH for the current to flow which means that there is LESS opposition to the flow of current coming from the power source. So the overall resistance in the circuit has decreased.

But by how much has it decreased?
Well, it must have decreased down to at least "the path of least resistance", mustn't it? So, in the example above, the resistance must have dropped at least as low as 5 Ω.
In fact, since there are now 2 paths, the overall resistance will be somewhat lower than 5 Ω.

Anyway, all we need to remember is that the overall resistance, for resistors in parallel, is less than the resistance of the smallest resistance.

Quick Question Point 3:

In the circuit above, is the overall resistance approximately 2 , 200 or 2 K (2,000) ohms ? Just type the number, not the unit. Check