Basic electric circuit theory

Circuit theory provides the rules for predicting how voltages and currents distribute themselves in a network of connected components. It treats a circuit as an arrangement of elements such as sources, resistors, capacitors and inductors joined by ideal conductors, and uses a small number of laws to calculate the behaviour at any point. These methods underpin the analysis and design of every electrical and electronic system.

The most fundamental relationship is Ohm's law, which states that the voltage across a resistor equals the current through it multiplied by its resistance. Two further rules, known as Kirchhoff's laws, complete the basic toolkit. Kirchhoff's current law states that the total current entering any junction equals the total current leaving it, expressing the conservation of charge. Kirchhoff's voltage law states that the voltages around any closed loop add up to zero, expressing the conservation of energy. Together these allow the currents and voltages in any resistive network to be found.

Components combine in predictable ways. Resistors in series add directly, because the same current flows through each and their voltage drops accumulate. Resistors in parallel combine so that the total resistance is less than the smallest, because the current divides among them. The electrical power dissipated or delivered is the product of voltage and current, measured in watts, and for a resistor can also be written in terms of resistance. From these few principles, more advanced techniques such as nodal and mesh analysis and the use of equivalent circuits are derived.

Frequently asked questions

What is Kirchhoff's current law?

It states that the total current flowing into any junction equals the total current flowing out, which follows from the conservation of electric charge.

How do resistors combine in series and parallel?

In series their resistances add directly, while in parallel they combine so the total is less than the smallest individual resistor, because the current splits between them.

How is electrical power calculated?

Power is the product of voltage and current, measured in watts; for a resistor it can also be expressed using its resistance and either the current or the voltage.