A circuit containing ideal voltage sources and resistors can be solved by combining Ohm's law with Kirchhoff's laws.

Series resistors

Components are in series when the same current passes through them. For resistors,

$$R_{\mathrm{eq}}=R_1+R_2+\cdots.$$

The source voltage is divided among the series resistors according to their resistances.

Parallel resistors

Components are in parallel when they share the same two nodes and therefore the same voltage. For resistors,

$$\frac1{R_{\mathrm{eq}}} =\frac1{R_1}+\frac1{R_2}+\cdots.$$

The branch currents add to the total current.

General networks

Not every resistor network reduces by obvious series-parallel combinations. In a general circuit, assign branch currents or node voltages and write enough independent Kirchhoff equations together with

$$V=IR$$

for each resistor.

Checking a solution

Calculated currents and voltage drops should satisfy charge conservation at every node and zero net voltage change around each loop. Power supplied and dissipated also provide a useful consistency check.

Circuit analysis is therefore a structured application of conservation laws and component models, not a collection of unrelated resistor formulas.