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

Motor

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:

Battery

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
flashlight

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.)

Resistors

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:

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:


resistor

Rtot = 9 Ω + 9 Ω + 9 Ω = 27 Ω

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

resistor

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:


resistor

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

Summary