Three steps

There are three steps in this episode.

• In the first step an extra battery is added to the circuit. This is compared to the simple circuit studied up to this point.
• Then, this same simple circuit is compared to one where there are two bulbs in a single loop.
• Finally, the simple circuit is compared to one in which there are two bulbs, but each is on its own loop.

So what do you do and what happens?

What happens when a second battery is added to the circuit so that we now have two batteries and one bulb?

There are many equivalent ways of drawing this circuit – here we'll consistently prefer one, shown in the centre of the diagram. They are equivalent because the loop contains the same number of cells driving the current and the same number of bulbs impeding the current.

When the circuit is completed, the bulb lights up and it is now brighter than normal. How can we explain this observation using the electric circuit model?

A larger current

The first effect is simply that there is a larger current; adding more batteries increases the current in every element in the loop.

Notice that the current is the same everywhere in the loop.

Thinking about the electric circuit model

Adding a second battery to the circuit has the effect of producing a bigger push from the two batteries acting together, moving the charged particles around the circuit more quickly. This means that more charged particles per second pass any point in the circuit and so the size of the electric current is increased. It is worth emphasising here that the number of charged particles moving around the circuit has neither been reduced nor increased. The same charged particles simply drift faster because of the extra battery.

There are two effects that contribute to the bulb being brighter. The batteries maintain the faster motion of the charged particles, so that:

The number of charged particles passing through the filament of the bulb per second increases, and Each charge shifts more energy as it passes through the filament of the single bulb.

The model to develop is one where adding the extra battery results in more charged particles passing through the bulb per second, with each shifting more energy. So more energy is shifted in each second and the bulb is brighter.

Find out what makes the bulb brighter

It is interesting to look in more detail at what happens in the circuit when an extra battery is added.

First of all, think about the charged particles as they are driven by the push of a single battery through the filament of the bulb. Each charge is both driven and retarded as it moves through the array of fixed ions. The interaction with the ions retards the charge. The driving forces are provided by the remote action of the battery. As the ions are spaced out the charge travels a short distance before interacting with the next ion. Therefore the motion is not steady, as the retarding and driving forces vary with the position of the charge.

With an extra battery, the positive terminal of the battery becomes more positively charged and the negative plate becomes more negatively charged, creating a greater force on the charged particles.

As a result:

• More charged particles pass through the filament each second
• More energy is shifted by each passing charge.

So what do you do and what happens?

What happens when a second bulb is added to the circuit, so that we now have one battery and two bulbs all connected in series, in one single loop?

When the circuit is completed, both bulbs light up. However, this time they are not as bright as the single bulb: they are now equally dim. How can we explain this observation using the electric circuit model?

The effect of adding the second lamp

The effect of adding a second bulb in series is to increase the overall resistance of the circuit. The resistance previously provided by the thin filament wire of just one bulb is now doubled due to the presence of two.

This increase in resistance reduces the drift speed of charged particles everywhere in the circuit. Fewer charged particles per second pass any point in the circuit so the size of the electric current is reduced.

It is worth emphasising here that the total number of charged particles moving around the circuit has neither been reduced nor increased.

The charged particles have simply been slowed down all around the circuit by adding resistance.

Two equal resistances: equal energy dissipated in each

Given that there are now two equal resistances in the circuit, and bearing in mind that energy is shifted wherever there is an electric current in a resistance (first met in episode 01) you should focus on the resistances. These are equal, so the forces on the charged particles in these resistances will be equal. What else could they be? So the same amount of energy is shifted at each resistor: same push and pull on each charge; same number of charged particles passing through each resistor.

There is no difference: the resistors or bulbs are identical, so what other possibilities need we consider?

The bulbs are dimmer because adding the extra bulb increases the resistance and reduces the current everywhere in the whole circuit.

As a result fewer charged particles per second pass through each bulb and each charge shifts less energy as it passes through the filament.

Find out what makes the bulb dimmer

It is interesting to look in more detail at what happens in the circuit when an extra bulb is added.

With an extra bulb, the total resistance in the circuit is increased so the charged particles move around more slowly. This results in:

• A decrease in the number of charged particles passing through the filament each second
• Less energetic interactions with the fixed ions (each collision shifts less energy to the ions) in both bulbs.

So, both bulbs in the circuit become dimmer as a result of the second bulb being added because fewer charged particles per second pass through each bulb and the interactions between charged particles and lattice ions are less energetic.

So what do you do and what happens?

Starting point: what happens when a second bulb is connected in parallel with the first?

When the circuit is completed, both bulbs light up, and each is of normal brightness (the same as with one battery and one bulb). When first encountered, this effect can seem a bit surprising, almost as if something is being gained for nothing.

Just by connecting the bulbs in parallel, they both shine with normal brightness. How can we explain this observation using the electric circuit model?

A current in both loops

Adding a second bulb in parallel to the first sets up a second circuit loop in which charged particles can be set in motion. Not only do we have the loop of charged particles passing through the first bulb, but we also have a second loop of charged particles flowing through the second bulb. The number of charged particles passing through the battery each second is thus doubled, with equal contributions from each separate, independent loop.

In other words, the current in the battery is double that with one battery and one bulb, whilst the current in each bulb is the same as in a circuit with one battery and one bulb.

In each loop of the circuit, the charged particles are set into motion by the battery and are shifting energy to the surroundings as they pass through the filament.

Two bulbs of normal brightness

When a second bulb is added in parallel the electric current in each bulb is the same as the circuit with one battery and one bulb. As the loops are independent, each functions exactly as the single loop. The two bulbs are symmetrical, and so both bulbs are of equal brightness (and of the same brightness as one bulb in a single loop, precisely because that is what they are).

Connecting bulbs in parallel does not get you something for nothing, even though at first sight this might appear to be the case! The good news is that we have two bulbs of normal brightness. The bad news is that the energy in the chemical store of the battery is depleted twice as quickly as with one bulb. The electric circuit model confirms this point of view because the electric current in the battery (the flow of charged particles shifting energy) is doubled as the second bulb is added in parallel.

Either make more loops, or change one loop

• adding cells or batteries in series increases the current
• adding cells or batteries in parallel makes them last longer
• adding resistors or bulbs to a single loop (so necessarily with series connections) decreases the current in the battery
• adding loops by adding more resistors or bulbs using parallel connections increases the current in the battery

In each case the current is set by the push provided by the batteries and the resistance of the other elements in the loops.