Electric Circuits

racing circuit

No, not a racing circuit, an electric circuit:

electric circuit

The battery provides power to the motor, and is wired like this:

electric circuit


The motor spins and can be used to do cool things like make wheels turn, or as part of a drill, or to make robots move. Wonderful things.

A motor:


The battery holds electric charge and has a voltage which can be thought of as like water pressure:

When the switch is on, the battery voltage makes the current flow.

Voltage, current and resistance are related this way:

V = IR
Ohm's Law

The units are:

It must have gone VIRal when they discovered it!

Let's use it:

Example: The motor needs 1.5 A current. What voltage should the battery have?

The motor needs 1.5 Amps and has 8 Ohms resistance, so:

V = IR
= 1.5 A × 8 Ω
= 12 V

So a 12 V battery will work.

Ohm's Law

The Relationship V = IR is called Ohms's Law. There are 3 ways it can be written:

V = IR         I = VR         R = VI

They are just rearrangements of each other using algebra.

The middle one shows us that more voltage causes more current but more resistance causes less current:

I = V/R

Example: A flashlight has this circuit:

flashlight circuit

We can calculate the current:

I = VR = 3 V6 Ω = 0.5 A

If we replace the LED with a 15 Ω one we get:

I = VR = 3 V15 Ω = 0.2 A

More resistance means less current.

Now let's upgrade the battery with a 9 V one:

I = VR = 9 V15 Ω = 0.6 A

More voltage means mor current.

(Note: there are "non-Ohmic" components like diodes and transistors that don't obey Ohm's Law V = IR.)


You find a new LED with only 3 Ω resistance. And you want to use a 3 V battery, so the current would be:

I = VR = 3 V3 Ω = 1 A

But the LED only needs 0.2 A, so you need extra resistance.

Not a problem! We can add a resistor:


Resistors just provide resistance.

We place a 12 Ω resistor in the circuit like this:

flashlight circuit 2 resistances

Because the 12 Ω resistor is followed by the 3 Ω LED (ie they are in series) we simply add the two resistance values:

12 Ω + 3 Ω = 15 Ω

And our current is now:

I = 3 V15 Ω = 0.2 A

Just as we want.

Series and Parallel

Resistors that follow one another are in series and can be simply added:

Rtot = R1 + R2 + ...

Example: What is the total resistance here:


Rtot = 9 Ω + 9 Ω + 9 Ω = 27 Ω

But when they are side-by-side they are in parallel, and the calculations change.


The current can flow through them at the same time. More current goes through the lower resistor, and the calculation is:

1Rtot = 1R1 + 1R2 + ...

It is like we are adding but in reciprocal land.

Example: What is the total resistance here:


1Rtot = 14 + 112
1Rtot = 312 + 112
1Rtot = 412 = 13

So Rtot = 3 Ω

Or we can do it in one go (using a calculator):

Rtot = 1/(14 + 112) = 3 Ω

It is OK to use a calculator, and to round the results, as a good resistor is only within 1% of its stated value (called "tolerance"), some can be less accurate.

Both Together

For more complicated cases we calculate parallel resistance before we add them in series:

Example: What is the total resistance here:

resistor circuit

Start as far "inside" as we can - the three parallel resistors:

1/(14 + 112 + 112) = 2.4 Ω

Now add the 2 Ω resistor in series:

2 Ω + 2.4 Ω = 4.4 Ω

Now combine with the 3 Ω resistor:

1/(14.4 + 13) = 1.783... Ω

Answer: Rtot = 1.8 Ω

Other Components

There are many other Components in electric circuits, such as capacitors, speakers, diodes, etc.

Here are some of the more common symbols:

common circuit symbols