# Lesson 8: Parallel Circuits

## Introduction

In this lesson we'll look at parallel circuits. We'll see why they're so common. We'll also look at voltage, power, current and effective resistance.

## The advantage of parallel circuits over series circuits

If we want to connect two bulbs to the same battery then an obvious way to connect them is in series. This means that both bulbs are in the same conducting path from one terminal of the battery to the other.

The problem with connecting two bulbs in series is that both bulbs are dim and if you turn one bulb off then they both go off.

There are two advantages of connecting bulbs in parallel.

- They all get the full battery voltage so they're all bright
- They're all in their own conducting loop so you can turn one bulb off without affecting the others.

## Parallel circuits in the home

At home all your appliances are connected in parallel with each other. This means they all get the full mains voltage and you can turn on your TV without having to turn on your microwave as well.

How does this work?

The electric cables in your house contain three wires. We'll ignore the earth for the moment and just concentrate on two of them: the live and the neutral. In Europe the live is brown and the neutral is blue. In the US live can be black, red or yellow; and neutral tends to be white or white with yellow stripes.

There is a voltage between the live and neutral because they are indirectly connected to a power plant. Each electric socket in your home is connected to the live and the neutral. The metal pins of a plug make an electrical connection with the socket. A lead, again with live and neutral wires, connects the plug to your appliance.

Each appliance has its own connection between live and neutral so each appliance can be switched separately and has the whole live voltage across it.

## Adding things in parallel always increases the total current

Even though all the appliances in your home are connected across the same voltage, they'll all draw different currents. An electric oven transfers energy quickly so the current drawn by that will be big. The TV transfers energy quite slowly so the current drawn by that will be quite small.

All of these currents must add in the power supply since it has to provide them all at the same time. The more appliances that are connected the greater the current drawn.

## Why current doesn't 'split' at junctions in parallel circuits

It's quite common to say that current splits at junctions in parallel circuits but you need to be very careful with this idea. It can often lead to the constant current misconception.

The first point to remember is that the charges don't start from the battery and then flow through empty wires until they come to a junction and then have to decide what to do. The charges are already there everywhere in the circuit and they all start flowing very slowly everywhere at the same time.

The other issue is that there isn't a 'the current' to flow. The more things you connect in parallel the greater the current drawn from the power supply. The same current doesn't just split differently.

It's sometimes easier to think of the components as active things demanding current from the power supply. If the circuit is set up so that sometimes these currents have to flow through a single wire then you have to add them up.

## Calculating currents in parallel circuits

When bulbs are connected in parallel they must have the same voltage across them. You can treat them as if they're each in their own circuit (which if you treat circuit as meaning loop, they are).

If the bulbs are different then the lower resistance one will draw the bigger current and be brighter. This is just Ohm's law: small resistance means big current.

This is the strategy:

- calculate the current through each bulb using Ohm's law
- add the currents to find the current drawn from the battery

You can calculate the current using the Ohm's law equation V = IR. First you need to rearrange it so I = V/R and remember that V is just the battery voltage.

## Adding things in parallel always decreases the effective resistance

The battery of a parallel circuit doesn't 'know' what's connected to it. All it feels is an overall resistance (or if you like an overall demand for current). The resistance that the battery feels is called the effective resistance of the circuit.

As you add more and more components in parallel the current drawn from the supply gets bigger and bigger. If the current gets bigger then the resistance must be getting smaller. So by adding resistances you actually decrease the effective resistance, which seems odd.

It doesn't matter how enormous the resistance is, adding it in parallel always make the effective resistance go down. There are a couple of analogies for explaining this.

If you have a bath with a hole in the bottom it will empty. If you add another hole, no matter how small, the bath will always empty quicker.

Or think of a huge crowd leaving a sports stadium through the main gates. If even a tiny side-gate is also opened then the number of people leaving the stadium each minute goes up.

## Rules of thumb for calculating effective resistance of parallel circuits

- The overall resistance is always less than the smallest resistance (because you can always imagine building the circuit with the smallest resistance first and then the effective resistance continuing to decrease as you add the bigger resistances).
- Two identical resistors have an effective resistance of half their value (because adding the second resistance doubles the current, so halves the resistance).
- Three identical resistors have an effective resistance of a third of their value and so on.
- A very big resistance and a very small resistance in parallel has an effective resistance of a little less than the small resistance (the small resistance is like a big hole in a bath, adding another tiny hole still increases the overall flow rate a tiny amount)

## Calculating the effective resistance of parallel circuits

The formula for calculating the effective resistance of parallel circuits looks quite complicated, which is possibly why parallel circuits are often taught after series circuits, even though parallel circuits are far more common and far more useful.

This formula can be fairly easily derived if you don't mind dealing with fractions.

Using the formula is not too difficult. Simply substitute in your values for the resistances and then add up the fractions.

Beware, after you've added up the fractions you end up, not with R_{effective}, but 1/R_{effective} so you need to turn your result upside down to find the effective resistance.

As a check, make sure that the result is smaller than the smallest resistance.

## Calculating effective resistance by calculating the total current drawn

Rather than using the formula we can calculate the total current drawn from the power supply and then use R_{effective} = V_{battery}/I_{total} to calculate the effective resistance.

This is effectively what the formula does but sometimes a question will give you currents through the components, rather than their resistances so it's quicker to use this method, rather than to calculate the resistances first and then use the formula.