Electric circuits can be defined as closed or continuous paths in which electric currents are confined and around which electric currents can be caused to flow. Electrical circuits are an essential part of daily living, and may be found in heavy and light industry, commercial installations and operations, and residential applications. Modern life and its many conveniences seem inconceivable without the use of electric circuits.
The total resistance of a circuit is the sum of the individual resistances of the power source, the wiring, and the load. The load resistance is generally much higher than either the resistance of the power source or the wiring. The resistances of the wiring are usually neglected in classroom laboratory experiments. Very rarely is circuit wiring significant in experimental work. In these cases we consider the loads resistances to be the only resistance. Wiring resistance may be considerable in the case of transmission cables, as well as telephone lines, which are many miles long, and we have a lab which investigates and calculates the resistance in such cables and the lost power and energy due to these lengths.
If an arbitrary load of relatively low resistance were connected to an existing power supply or voltage source, an excessive current might flow to the load, causing burn up or other malfunctions with the load and wiring. The current can be reduced
by reducing the source voltage, but this is not always feasible and is frequently impossible. The resistances of the voltage source or the load could be increased, but these are usually built right into the source or load. Resistances of connecting wires are so low that miles would be needed to increase the circuit resistance by more than a few dozen ohms. A selection of materials for connecting wires might be useful, but a better method would be to creation of a device that is specifically a resistor that can be included with the circuit to give the net or total resistance needed to provide the desired current for the voltage source involved.
In any DC circuit, the total current is equal to the power source voltage divided by the total or equivalent resistance. For a Series Circuit, this is the only current. This means that if the current in some portion of the circuit is known, the total current and the current through every part of the circuit is known. The sum of the voltage drops across the resistors in series is equal to the power supply voltage.
In Parallel Circuits, the total current from the power source divides into different paths as in approaches the parallel branches. The voltage drop across parallel branches is the same for all the branches. If the voltage drop for one branch is known, the voltage drop for all the parallel branches is known. The sum of the currents in the various branches is equal to the current from the power supply.
Circuits with combinations of Series and Parallel portions or sections are more complex. The current through different sections is not the same and the voltage drop across various branches is not the same either.
Ohm's law is the relationship between voltage, current, and resistance, and is used to calculate current, voltages, or resistances in relatively simple circuits that may be reduced to a simple circuit consisting on one voltage source and on resistance. For more complex circuits, including series and parallel portions and branches that might not be reducible or readily reducible to a single resistor, the application of Kirchhoff's Rules is used to solve for various branch currents, branch voltages, total current and power.
Kirchhoff's Rules are two, the Junction Rule and the Loop Rule. The Junction Rule says that the sum of currents entering a node must equal the sum of currents leaving the node. The Loop Rule says that the sum of the voltage sources around a loop must equal the sum of the voltage drops or i*R drops around the same loop. Algebraically these would be:
Σ i = 0.0 (Node Rule) and ΣV = Σ i*R or Σ V - Σ i*R = 0.0
Various sections are from Total Circuit Resistance: Mileaf, 7th ed pages 2-20, 2-22, 2-106