27.4 : Combination Of Resistors

Electrical devices in any circuit can be connected either by series or parallel connections. Additionally, circuits can be connected involving both of these connections, known as combination or complex circuits. As these circuits have complex resistor connections, it is necessary to identify different parts as either series or parallel connections, then the whole combination of series and parallel resistors can be reduced to a single equivalent resistance. With the known equivalent resistance and the total voltage, the total current in the circuit can be determined using ohm's law. This current is distributed to all resistors.

To obtain the current across each resistor, we need to consider the original circuit. If the resistors are connected in series, the current remains the same; if they are connected in parallel, the current divides as per the resistance value. Finally, the voltage drop across each resistor can be determined using Ohm's law with the known current values and the resistors' values.

Complex connections are common when the wire resistance is taken into consideration. In such a scenario, wire resistance is taken in series with other resistances that are in parallel. The resistance of the wires reduces the current value and hence the power delivered to the resistor. If wire resistance is comparatively large, as in the case of a very long wire, this loss can be significant. If a large current is drawn, the IR drop in the wires can also be substantial and may become apparent from the heat generated in the cord.