====== Resistor circuits ======

**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 [[ohms_law|Ohm's law]] and Kirchhoff's circuit laws.

===== Series and parallel =====

Series resistors carry the same current. Parallel resistors share the same voltage between their two common nodes.

<code>
Series:       R_total = R1 + R2 + ...
Parallel:     1 / R_total = 1 / R1 + 1 / R2 + ...
Two parallel: R_total = R1 R2 / (R1 + R2)
</code>

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.

===== Voltage divider =====

With R1 between the supply and the output, and R2 between the output and ground:

<code>
V_out = V_in R2 / (R1 + R2)     (unloaded divider)
</code>

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.

===== Practical considerations =====

Tolerance, temperature coefficient and [[electric_power|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.

===== References =====

  * [[https://openstax.org/books/university-physics-volume-2/pages/10-2-resistors-in-series-and-parallel|OpenStax: resistors in series and parallel]].
  * [[https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules|OpenStax: Kirchhoff's rules]].