\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \tau{\uptau}\) \(\def \ten#1{\times 10^{#1}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\) \(\def \ccw{\circlearrowleft}\) \(\def \cw{\circlearrowright}\)
Chapter 16: Circuits
2.

Batteries

Batteries are specifically designed to do one thing: maintain a potential difference $\Delta V$ between their terminals. This may surprise you: "I thought batteries were supposed to store and supply energy? Or maybe current?" It's true batteries do both those things, but only in the service of their primary function. If you hold a AA battery in your hand, and it's not connected to anything, it won't produce any current or any energy, but there is still a potential difference between its terminals.
The emfs of some common battery types. The terminal marked + is \(\cal E\) volts higher than the terminal marked -.

The potential difference across the terminals of a battery is called its emf $\cal E$, and is measured in volts. If you chain up multiple batteries, like in the last example, then their emfs add. For the "ideal batteries" we'll use in our problems, two batteries with the same emf will be identical, but in real life that is not the case. A C battery and a AA battery have the same EMFs, for instance, but a C battery will run for much longer before dying. Eight AA batteries have the same EMF as one car battery, but you won't be able to start your car with them: because of their internal resistance, they can't provide the same amount of Power.

The schematic symbol for a battery consists of two parallel lines, one longer than the other. The longer line is always the higher potential, what we call the "+" end of the battery, and is sometimes labelled as such to avoid confusion. Stacks of batteries are sometimes drawn instead of a single battery, but practically have the same meaning.

A sketch of a typical power supply.

Physics labs typically use power supplies instead of batteries. These function pretty much the same way in circuits, and may even use the same symbol, but their EMF is adjustable and they can be turned on and off, which of course is convenient for measurements. Power supplies may have more advanced features as well, such as the ability to limit the total amount of power it produces to protect equipment and users.