Resistor circuits combine resistors to set current, divide voltage, terminate signals or dissipate energy. Simple series and parallel networks can be reduced to an equivalent resistance using Ohm's law and Kirchhoff's circuit laws.
Series resistors carry the same current. Parallel resistors share the same voltage between their two common nodes.
Series: R_total = R1 + R2 + ... Parallel: 1 / R_total = 1 / R1 + 1 / R2 + ... Two parallel: R_total = R1 R2 / (R1 + R2)
For example, 100 Ω and 200 Ω give 300 Ω in series or approximately 66.7 Ω in parallel. Two equal resistors in parallel have half the resistance of either one.
At a junction, the sum of incoming currents equals the sum of outgoing currents. Around a closed circuit loop, the signed voltage changes sum to zero. These statements are useful checks on a circuit calculation.
With R1 between the supply and the output, and R2 between the output and ground:
V_out = V_in R2 / (R1 + R2) (unloaded divider)
A 10 kΩ upper resistor and 10 kΩ lower resistor give 6 V from 12 V if no significant current is drawn from the output. Connecting a 10 kΩ load across the lower resistor changes that lower branch to 5 kΩ, so the output falls to 4 V. A divider is therefore not a general replacement for a regulated power supply.
Tolerance, temperature coefficient and power dissipation affect a real circuit. At radio frequencies, leads and construction introduce inductance and capacitance. A component that is a suitable DC resistor may be unsuitable as an RF termination.