Series R

When current flows through one resister and then another we say the resistors are in series.

R = R1 + R2 says sum the resistance to get the Lumped R.

To find the voltage dropped by either resistance, first find the current (I) through the lump, then use E = IR to find individual voltage drops.

E = E1 + E2 says the voltage drop across the lump is the sum of the voltage drops across each series resistor.

A circuit that feeds (almost) all current through series resistors is called a voltage divider. If R1 connects to your signal, and R2 connects to ground, then the voltage output from the middle of the circuit is a small proportion of the voltage in.

Eout = Ein R2 / (R1 + R2)

A voltage divider that leaks significant current into the next stage of the circuit can be analyzed by treating the input resistance of the following stage as a Parallel R with R2

Factoids

A potentiometer creates a voltage divider by taping the voltage drop at a variable spot along a fixed resistance. Take one apart. You can see how it works.

A potentiometer used as a volume control will use unevenly applied resistance material. This compensates for the physiological fact that our sense of loudness is equally uneven. These might be called "audio taper" potentiometers while the uniform ones would be called "linear taper" potentiometers.