# 7.08 Superposition theorem.

Consider the circuit shown below. The superposition theorem gives a method for finding the currents in the circuit, which then enables all the voltage drops to be calculated. The procedure is described below.

• Redraw the circuit for each e.m.f. in turn shorting out the other e.m.f .
• Calculate the currents that would flow due to each e.m.f. acting alone.
• Finally add the branch currents from each of the circuits (taking into account their direction*) to find the branch currents for the original circuit.
• Use these currents to find the voltage drops in the original circuit.

* Note, to add the branch currents while taking into account their direction, may actually require one current to be subtracted from another. i.e. If both currents are flowing in the same direction, you simply add them, but if the currents are flowing in opposite directions, you subtract the smaller current from the larger one. The resultant current will flow in the same direction as the larger current.