Summarizing Kirchhoff’s Rules

Summary

• Kirchhoff’s rules can be used to analyze any circuit, simple or complex.
• Kirchhoff’s first rule—the junction rule: The sum of all currents entering a junction must equal the sum of all currents leaving the junction.
• Kirchhoff’s second rule—the loop rule: The algebraic sum of changes in potential around any closed circuit path (loop) must be zero.
• The two rules are based, respectively, on the laws of conservation of charge and energy.
• When calculating potential and current using Kirchhoff’s rules, a set of conventions must be followed for determining the correct signs of various terms.
• The simpler series and parallel rules are special cases of Kirchhoff’s rules.

Glossary

Kirchhoff’s rules

a set of two rules, based on conservation of charge and energy, governing current and changes in potential in an electric circuit

junction rule

Kirchhoff’s first rule, which applies the conservation of charge to a junction; current is the flow of charge; thus, whatever charge flows into the junction must flow out; the rule can be stated \({I}_{1}={I}_{2}+{I}_{3}\)

loop rule

Kirchhoff’s second rule, which states that in a closed loop, whatever energy is supplied by emf must be transferred into other forms by devices in the loop, since there are no other ways in which energy can be transferred into or out of the circuit. Thus, the emf equals the sum of the \(\text{IR}\) (voltage) drops in the loop and can be stated: \(\text{emf}=\text{Ir}+{\text{IR}}_{1}+{\text{IR}}_{2}\)

conservation laws

require that energy and charge be conserved in a system