  The way in which electric power depends on the topology of circuits with
mixed voltage and current sources is examined. The power flowing in any
steady-state DC circuit is shown to depend on a minimal set of key variables
called fundamental node voltages and fundamental edge currents. Every
steady-state DC circuit can be decomposed into a voltage controlled subcircuit
and a current controlled subcircuit. In terms of such a decomposition, the I^2R
losses of a mixed source circuit are always the sum of losses on the voltage
controlled subcircuit and the current controlled subcircuit. The paper
concludes by showing that the total power flowing in a mixed source circuit can
be found as critical points of the power expressed in terms of the key voltage
and current variables mentioned above. The possible relationship to topology
control of electric grid operations is discussed.
