# Engineering Principles V11

Clive W. Humphris

CIRCUIT THEOREMS: Superposition Theorem 1. When a circuit has multiple sources of voltage the current flowing at any one point will be a sum of the currents from each source and each power supply will act like a short circuit on another power supply. In this example the R3 current is made up of electrons from both batteries. Each battery contribution will depend on the source voltage and the associated resistor values.

Applying the Superposition theorem means we consider the each half of the circuit as if it is supplied from one source, i.e. V1 with V2 shorted and then V2 with V1 shorted. The potential difference across R3 will be a sum of these quite separate calculations.

The effect of shorting out the battery is to place the resistor on that side of the circuit in parallel with R3. Remember their combined value will always be lower than the smallest one. The voltages Va and Vb at the potential divider junctions are then calculated and added. This is the resultant voltage across R3.

Circuit currents can be found by applying Ohm's Law. 