Foundations — Series and parallel resistance

Before you can read the parent note Series and parallel resistance, every letter and squiggle it uses must mean something physical to you. This page builds each one from nothing, in an order where each idea leans on the one before it.

1. Charge — the stuff that flows

The picture: imagine a pipe filled with countless little marbles. The marbles are the charge. Nothing yet says they move — right now they just sit there, ready.

Why the topic needs it: without something to flow, "resistance" would have nothing to resist. Charge is the actor; everything else describes how it behaves.

2. Current $I$ — how fast the charge flows

Why a rate and not just "amount"? Because circuits are about flow. Asking "how much charge is in the wire" is like asking "how much water is in the river" — not useful. What matters is "how much passes this spot each second", exactly like litres per second in a river. That is why we divide charge $Q$ by time $t$: the division turns a total into a flow.

The picture: count how many marbles cross a chalk line drawn across the pipe in one second. That count is the current. A fat, fast stream = big $I$; a thin, slow trickle = small $I$.

3. Voltage $V$ — the push

Why "difference"? Water flows downhill because one end is higher than the other — it's the difference in height that matters, not the absolute height. Voltage is the electrical version of that height difference. A battery is a pump that lifts the water back up, keeping a permanent "waterfall" of $V$ across its terminals.

The picture: a tilted pipe. The steeper the tilt (bigger $V$), the harder the marbles are shoved along.

4. Resistance $R$ — the obstacle

The picture: a narrow, gritty choke in the pipe. For the same tilt (voltage), a tighter choke lets fewer marbles through per second (less current). That "tightness" is $R$.

Why the topic needs it: the entire chapter is about combining these chokes and asking "what single choke behaves like the whole set?" You cannot ask that until $R$ has a clear meaning.

5. Ohm's law — tying push, flow, and obstacle together

Why we need it: it is the bridge between the three quantities. Given any two, it hands you the third. Every single derivation in the parent note starts by writing $V=IR$ for one resistor. Read the full story at Ohm's Law.

The picture: the tilted-pipe-with-a-choke. Steeper tilt ($V\uparrow$) pushes more marbles per second ($I\uparrow$). Tighter choke ($R\uparrow$) holds them back ($I\downarrow$). Ohm's law is just those two arrows written as an equation.

6. Nodes, junctions, and the two Kirchhoff rules

This distinction is the whole secret of telling series from parallel, so we make it visual.

Why two laws? They answer the two different questions the topic keeps asking:

• KCL governs how current shares out → gives the parallel rule.
• KVL governs how voltage shares out → gives the series rule.

The full derivations live in Kirchhoff's Laws. Here, just hold the pictures: marbles conserved at a fork (KCL), tilt adds up around a loop back to start (KVL).

7. Reading the formulas' notation

Before the parent note's boxed results make sense, three pieces of shorthand:

8. The prerequisite map

Quick sanity example

Equipment checklist

Test yourself — cover the right side. If any line is fuzzy, reread its section above.

Connections

• Ohm's Law — the $V=IR$ bridge built in §5.
• Kirchhoff's Laws — the KCL/KVL of §6 in full.
• Resistivity and Resistance — where a single $R$ comes from ($R=\rho L/A$).
• EMF and Internal Resistance — a real battery's own resistance sits in series.
• Wheatstone Bridge — networks that are neither pure series nor parallel.
• Power in Circuits — once $I$ and $V$ are known, power follows ($P=IV$).