# 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:

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**I**ntensity) - 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 Ohms's Law. There are 3 ways it can be written:

V = IR I = \frac{V}{R} R = \frac{V}{I}

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 = \frac{V}{R} = \frac{3 V}{6 Ω} = **0.5 A**

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

I = \frac{V}{R} = \frac{3 V}{15 Ω} = **0.2 A**

More resistance means less current.

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

I = \frac{V}{R} = \frac{9 V}{15 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 = \frac{V}{R} = \frac{3 V}{3 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 = \frac{3 V}{15 Ω} = **0.2 A**

Just as we want.

### Series and Parallel

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

_{tot}= R

_{1}+ R

_{2}+ ...

**R**is the total resistance_{tot}**R**are the individual resistances_{1}, R_{2}, etc

### Example: What is the total resistance here:

_{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:

So R_{tot} = 3 Ω

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

_{tot}= 1/(\frac{1}{4} + \frac{1}{12}) = 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:

Now add the 2 Ω resistor in series:

Now combine with the 3 Ω resistor:

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 = \frac{V}{R}
- R = \frac{V}{I}

- Resistors in Series: R
_{tot}= R_{1}+ R_{2}+ ... - Resistors in Parallel: \frac{1}{R_{tot}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + ...