Electric Circuits

No, not a racing circuit, an electric circuit:

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

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:

• needs electrical current to run
• and has electrical resistance

Battery

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

This is the Electricity Water Analogy

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

Voltage, current and resistance are related this way:

Ohm's Law

The units are:

• Voltage: V for Volts
• Current: A for Amps   (in formulas: I for current Intensity)
• Resistance: Ω for Ohms

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 Ohm'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:

Example: A flashlight has this 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. Andyou 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:

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

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:

• R_tot is the total resistance
• R₁, R₂, etc are the individual resistances

Example: What is the total resistance here:

R_tot = 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:

It is like we are adding but in reciprocal land.

Example: What is the total resistance here:

1R_tot = 14 + 112

1R_tot = 312 + 112

1R_tot = 412 = 13

So R_tot = 3 Ω

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

R_tot = 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:

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: R_tot = 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:

Summary

• Ohm's Law:
  • V = IR
  • I = VR
  • R = VI
• Resistors in Series: R_tot = R₁ + R₂ + ...
• Resistors in Parallel: 1R_tot = 1R₁ + 1R₂ + ...