27.14 : Power Dissipated in a Circuit: Problem Solving

The equivalent resistance of a combination of resistors depends on their values and how they are connected.

The simplest combinations of resistors are series and parallel connections. In a series circuit, the first resistor's output current flows into the second resistor's input; therefore, each resistor's current is the same. Thus, the equivalent resistance is the algebraic sum of the resistances. The current through the circuit can be found from Ohm's law and is equal to the battery's emf over the equivalent resistance. The potential drop across each resistor can be found using Ohm's law. The total power dissipated by the resistors is equal to the sum of the power dissipated by the source, as expected from the principle of conservation of energy.

In a parallel circuit, all the resistors' leads are connected. Each resistor has the same potential drop across it, but the currents through each resistor may be different and will depend on the resistor. The sum of the individual currents equals the current that flows into the parallel connections. A circuit with parallel connections has a smaller total resistance than the resistors connected in series. The total power dissipated by the resistors equals the power supplied by the source, which is expected from the energy conservation principle.