  This paper derives analytical closed-form expressions that uncover the
contributions of nodal active- and reactive-power injections to the active- and
reactive-power flows on transmission lines in an AC electrical network. Paying
due homage to current- and voltage-divider laws that are similar in spirit, we
baptize these as the power divider laws. Derived from a circuit-theoretic
examination of AC power-flow expressions, the constitution of the power divider
laws reflects the topology and voltage profile of the network. We demonstrate
the utility of the power divider laws to the analysis of power networks by
highlighting applications to transmission-network allocation, transmission-loss
allocation, and identifying feasible injections while respecting line
active-power flow set points.
