Common misconceptions about electricity
Batteries store charge
Because we talk about 'charging' a battery, it's a common misconception that batteries store electric charge or electrons.
This is tied up with another incorrect idea that an electric current is the flow of electrons through initially empty wires.
For every electron that leaves a battery at one terminal another one enters at the other, so batteries never run out of charge. What they run out of is the ability to make the charges everywhere in the circuit move. This is essentially because the chemicals that make the battery work have all reacted.
It's useful to think of batteries running out of energy.
The current takes the easiest route
This argument is often used to explain short circuits, and parallel circuits where the resistances are different.
It's a variation of the constant current misconception. The key idea is that there isn't a 'the current' which chooses a route. If you change a circuit then the current changes. The same current doesn't just 'split' differently.
Charges slow down as they go through a thin piece of wire
It's a common misconception that charges slow down as they go through the filament of a bulb because the filament is thinner than the wires in the rest of the circuit.
When road traffic goes through a bottleneck it slows down. But with charges the opposite happens. This is because the current has to stay constant. In other words the number of charges passing a point each second has to stay constant. If fewer charges can go side-by-side then they have to go quicker.
Quicker charges interact with the metal lattice more frequently and so this is where energy tends to get converted.
It's important to with this argument that there isn't a 'the current'. If you add a constriction to a circuit then the current everywhere is smaller.
The constant current misconception
This is one of the most enduring and widespread misconceptions and comes in many forms. The misconception tends to be implicitly rather than explicitly stated but the essential misunderstanding is that batteries want to produce a particular current.
In other words there is this current that wants to flow and circuits try and resist or split this current.
In other words people see batteries as constant current providers. In fact they are constant voltage providers (if you ignore internal resistance) and the current depends entirely on what you connect them to.
The problem normally rears its head when a circuit changes, for example an extra bulb is added in parallel, and the assumption is that the current drawn from the battery stays the same and simply splits differently.
In fact as soon as you change a circuit the current drawn from the battery changes.
High resistance bulbs are brighter than low resistance ones
Energy is converted in the filament of a bulb because it has a high resistance compared with the rest of the circuit. A wrong conclusion would be that the higher the resistance of the filament, the brighter it should be.
This comes from a feeling that the current has to 'try harder' to get through the bulb and so more energy must be transferred.
This is another symptom of the constant current misconception. The result of having a high resistance in a circuit is not that 'the current' has to struggle to get through but simply that the current would be less than it would otherwise be. If the resistance is very high then the current is nearly zero and hardly any energy is transferred at all.
But high resistance bulbs are dimmer because the current through them is smaller for a given voltage. Smaller current means charges with energy arrive slower and so energy is transferred slower.
Thick wires have a lower resistance because the charges have more space
If you believe that charges move through empty wires then it makes sense that the charges must move quicker when the wire is wider because there's more space.
This isn't what happens. The wire is already full of charges no matter how thick it is. The lattice of positive ions completely fills the wire because that's what the wire is made from. Having a thicker wire doesn't create more gaps.
In a given metal the speed of the charges depends only on the voltage. You can model a thick wire as lots of thin wires side by side. The current is bigger because each wire contributes charges passing a point each second. Bigger current for the same voltage means lower resistance.
An analogy is a three-lane road with the cars travelling at 30 mph has more cars passing a tree each second than a single-carriageway road with the cars travelling at the same speed.
Another way of looking at it is that for a given current the charges move slower if the wire is thicker. This means they transfer less energy to the lattice. In other words you need a smaller voltage for a given current. Hence lower resistance.
Charges move very quickly through empty wires
A common story is that electrons start at the negative terminal of a battery, race at nearly the speed of light through empty wires, get slowed down by resistances, split at junctions and finally limp back to the positive terminal with just enough energy to make it.
This story seems to explain why lights come on immediately you flick the switch and is consistent with the idea that resistors 'resist the flow of current'.
A more scientific explanation is that the wires are already full of free electrons. They move along the wires very, very slowly but everywhere at the same time, like a wheel. Resistances tend to be places where the electrons speed up because, for example, they have to go through a narrower wire like a lightbulb filament. The faster moving electrons interact with the lattice more frequently and that's why energy is transferred where there's resistance.