Secrets for understanding circuits

Here are some rarely mentioned rules of thumb that you can apply to help you understand circuits - a lot of them are counter-intuitive, and are either unmentioned or misunderstood in other resources. They are really aimed at teachers - you should decide how many of them you want to reveal to your students.

Batteries are constant voltage providers

Batteries keep the p.d. across their terminals constant regardless of what you connect them to, as long as you don’t make them provide too big a current.

That’s why batteries are rated in volts, not amperes or watts.

The advantage of this is that a manufacturer of batteries doesn’t need to know in advance what they’re going to run, and designers of devices just need to design to a given potential difference, and let the battery provide energy at the correct rate.

Whenever the circuit changes, the current changes

The current a battery provides depends on what it’s connected to.

If you change what it’s connected to, by for example swapping a bulb for one of a higher resistance or switching in another arm of a parallel circuit, then the battery will keep the p.d. across its terminals the same but change the current it provides.

There isn’t some fixed current that a battery wants to provide that gets ‘resisted’ by circuit components.

Neither is it helpful to think that current ‘splits’ at junctions. If you have more components in parallel, the battery provides a bigger current - it doesn’t take some fixed current and then split it differently.

Circuit maths is hard because many quantities don’t vary independently

V = IR does not behave in the same way as, say, s = ut.

Speed and time can be varied independently, but current and resistance can’t. If you change the resistance then you automatically change the current, too.

Remember that batteries are constant voltage providers that change the current they supply in response to changes to the circuit.

That’s why I = V/R is the best way to write the relationship. It says that current depends on the battery and what it’s connected to.

Similarly for P = IV and P=I2R, V and I are not independent, and neither are R and I.

That means doubling the battery voltage quadruples power (because current doubles, too) and increasing resistance reduces power (because I squared goes down quicker than R goes up).

Heating happens where the resistance is…

In a simple circuit, the part that gets hot is the place where the resistance is high.

So heating happens in the thin filament of an incandescent bulb, not in the lower resistance wires in the rest of the circuit.

…but the higher the resistance, the less the heating

In a simple circuit, high resistance bulbs are dimmer than low resistance bulbs because there is less heating.

Batteries respond to ‘feeling’ an increased resistance by supplying a smaller current, so energy is shifted slower. This is the exact opposite of what the rope loop predicts.

Batteries are lazy. If you make things more difficult for them, they start giving up, not working harder.

Electrical resistance is not like friction

Electrical resistance is just a rather dodgy mechanical metaphor for a non-mechanical phenomenon that we’re stuck with for historical reasons.

The idea of electrical resistance has to tell a story about flow and a story about energy.

It’s good at the flow story, but bad at the energy story. When we encounter a resistance we generally work harder to overcome it - think walking over soft sand, or pushing through a crowd.

But this is not how batteries respond to a higher resistance. They provide a smaller current, work less hard and cause less heating. Remember that there isn’t a ‘the current’ that the battery wants to provide.

Electrons move faster in a resistance, not slower

Remember that the idea of ‘electrical resistance’ is really unhelpful - it gives you the wrong macroscopic idea that it behaves like friction, and the wrong sub-microscopic idea that it slows electrons down.

In a simple circuit we have a place that we want to get hot - for example a bulb filament - or that gets hot incidentally - like a carbon resistor. These places get hot because the electrons travel faster there than in the rest of the circuit.

The current is still the same everywhere, but if the wire is narrower - like the filament - or there are fewer free electrons - like with the carbon resistor - then electrons have to move faster for the same number to pass a point each second.

Faster moving electrons travel further in one second, so come across more of the lattice, so have more interactions and shift more energy. In the thicker wires, the electrons travel slower, so come across less of the lattice per second, have fewer interactions and shift less energy.

The energy of the interactions doesn’t depend on the drift speed of the electrons because they are already moving randomly at about 100,000 times faster than their progress through the circuit.

Electron speed doesn’t depend on filament thickness

This rule of thumb assumes you have a filament bulb, where the resistance of the filament is much, much higher than the leads, connected in a simple circuit with a battery.

If you use a bulb with a filament with twice the cross-sectional area then the resistance will be lower, the current will increase and the bulb will be brighter.

But the current in the filament is made up of twice as many electrons moving side by side at the same, speed rather than the electrons moving faster. It’s like a motorway with a 30 mph limit compared to a single lane road with a 30 mph limit. More cars pass a point per second on the motorway, even though the speed is the same.

This makes intuitive sense, because you can imagine two thin filaments in parallel. It’s clear that the speed of the electrons in each filament won’t change but twice as many charges per second will pass.

Batteries change the size of the current they provide by changing their chemical reaction rates

A battery provides a big current when its chemical reactions go quickly and a small current when they go slowly.

There are two types of chemical reactions, one at each terminal.

One reaction tends to produce excess electrons, the other reaction tends to require electrons. When the circuit is connected, the electrons that are already there in the wire can shuffle along, connecting the two reactions, and creating a virtuous circle of mutual give and take.

Energy equilibrium sets the current

As well as making electrons available to form part of the current (both adding and removing), the chemical reactions also make energy available to cause heating in e.g. a bulb filament. The faster the reaction rate, the faster energy is made available.

The instant the circuit is connected, the battery’s chemical reactions rapidly increase until the rate at which energy is shifted out of the system by the component (e.g. a hot bulb) is exactly the same as the rate at which energy is shifted into the system by the battery.

There is one and only one current where this can happen, and it is this boundary condition that sets the current for any given battery-component pair.

All changes happen (nearly) instantly everywhere

It’s not just when circuits are connected or disconnected that changes happen nearly instantly.

Any change to the circuit, for example changing a variable resistor or variable power supply, or switching another parallel arm in or out will set up new patterns of potential and current almost instantly everywhere.

We say that the signal speed is very high. It’s like the couplings between train carriages - any change to the speed of the train is reflected in the speed of all the carriages almost instantly.