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# Lesson 9: Series circuits

## Introduction

It two bulbs are in series then you have to go through both of them to get from one terminal of the battery to the other.  In other words there is only one conducting path.

In this lesson we'll see what the problems are with series circuits.  We'll find out about current, voltage and resistance and we'll also look at a special kind of series circuit called a potential divider.

## The problem with series circuits

If two bulbs are in series then there are two problems

1. Both bulbs are dimmer than they would be by themselves
2. You can't turn one bulb off without turning both off

## Why bulbs in series are dimmer

The bulbs are dim for two reasons:

1. The current going through them is smaller because two bulbs in series have a higher resistance than a single bulb.
2. Each charge only gives up some of its energy in each bulb, i.e. the p.d. across each bulb is smaller

If the bulbs are the same then each charges will give up half its energy.  Remember there is no 'first' bulb.  The charges are already there and they flow everywhere at the same time.  The current is the same all the way round a series circuit.

Imagine putting brakes all the way round a bicycle wheel.  You wouldn't say that any of the brakes was first.

Brightness depends on power.  Power depends on both voltage and current.  With two bulbs in series you halve the voltage and roughly halve the current so the power dissipated in each bulb, and hence the brightness, is roughly a quarter what it would be if the bulb was connected alone.

## How do the charges 'know' to keep some energy for the second bulb?

The key is that the current must be the same everywhere in the circuit.  You don't know what that current will actually be unless you calculate it but you do know that it can't be different in each bulb.

For the current to be the same then you need a big voltage across a big resistance and a small voltage across a small resistance.  Those two voltages must add up to the battery voltage.

When you connect the circuit, the electrons take a few millionths of a second to settle down into a stable current.  During this tiny fraction of a second the current may be different in different parts of the circuit.

But this causes some bunching up as big currents catch up with small currents.  When the electrons bunch up they repel each other more and this tends to even up the current again.  In this way the current quickly settles down to a stable value with the correct voltage distribution.  Remember even though this settling process is very quick the drift speed of the electrons is very slow.

If you look at this process in more detail then you'll see that the electron distribution actually happens at the surface of the wires.

## High resistance bulbs are brighter in series circuits

If two bulbs in series aren't identical then one bulb will be brighter than the other.  Brightness depends on both current and voltage.

Remember the current through both must be the same because the current is the same everywhere in a series circuit.  This means the voltage across the bulbs must be different for their brightnesses to be different.

The brightest bulb will have the biggest p.d. across it.  If a bulb needs a big p.d. for a given current then it must have a high resistance.  So in series high resistance bulbs are brighter because they have a bigger p.d. across them.

In parallel circuits low resistance bulbs are brighter because they have a bigger current through them for the same p.d.

## Variable resistors in series change both voltage and current

You can use a variable resistor, like a rheostat, to change the brightness of a bulb by connecting it in series.  When the resistor has a high resistance the bulb is dim.  When the resistance is low the bulb is bright.

As the resistance of a variable resistor increases the overall resistance of the circuit increases and so the current decreases.  But there's another effect: the variable resistor takes a bigger and bigger share of the battery voltage so the bulb takes a smaller and smaller share.

So the bulb gets dimmer for two reasons.  The current through it is reduced AND the p.d. across it is also reduced.

You'll find that it's very difficult to control the brightness of a bulb in a smooth way using a variable resistor in series.  The only way to do this is connect the circuit as a potential divider.

## The resistor p.d. plus the bulb p.d. equals the battery voltage

When the voltage across the resistor is big the voltage across the bulb is small.  These two voltages always add up to the battery voltage (if you ignore internal resistance).

This is just an example of the voltage law.  You need to be careful how you apply the voltage law when you look at circuits that combine series and parallel parts.

## Finding the effective resistance of series circuits

Finding the effective resistance of resistors in series is very simple: just add up the individual resistances.  You can show why this is fairly easily.

Adding resistors in series always increases the effective resistance.  A very big resistance in series with a very small resistance is effectively the same as the big resistance.

## Calculating voltage and current for resistors in series

There are several ways to approach this kind of problem.  A fairly fool-proof way is

1. Calculate the overall resistance, Reffective
2. Use V = IReffective for the whole circuit to calculate the current, which is the same everywhere
3. Use V = IR for each resistor to calculate the voltage across each resistor

As a check, make sure the sum of the voltages across each resistor equals the battery voltage.

You can also use ratios to find the voltages directly.

## Potential dividers

We've seen that connecting a variable resistor in series with a bulb can change its brightness but there are problems with this approach.

A better way to control the brightness of a bulb is to set up the variable resistor as a potential divider.

Potential dividers are often used with logic gates and amplifiers.

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