Electrical and Electronic Formulas

Circuit analysis rests on a compact set of mathematical relationships that describe how voltage, current, resistance, capacitance and inductance interact. The most fundamental is Ohm's law, which states that the voltage across a resistor equals the current through it multiplied by its resistance. Building on this, Kirchhoff's laws govern complete networks: the current law states that the currents entering a node sum to zero, and the voltage law states that the voltages around any closed loop sum to zero. Together they provide enough equations to solve any linear circuit.

Several theorems simplify the analysis of larger networks. Thevenin's theorem says that any linear two-terminal network can be replaced by a single voltage source in series with a resistance, while Norton's theorem gives the equivalent as a current source in parallel with a resistance; the two equivalents are interchangeable. The superposition theorem allows a circuit with several sources to be analysed one source at a time and the results added. Other results, including the reciprocity, compensation and maximum-power-transfer relations, address specific situations encountered in network design.

Formulas for energy-storage elements extend the analysis to alternating current and transients. Inductor and capacitor relations describe how these components store energy and oppose changes in current or voltage, and RLC formulas describe resonance and the behaviour of tuned circuits. Further reference relationships cover magnetic circuits, antenna dimensions, operational-amplifier gain expressions, and the Fourier series, which represents a periodic waveform as a sum of sinusoidal components and underpins frequency-domain analysis.

Frequently asked questions

What do Kirchhoff's laws state?

Kirchhoff's current law says currents entering a node sum to zero; his voltage law says voltages around any closed loop sum to zero. Together they let any linear circuit be solved.

How do Thevenin and Norton equivalents relate?

Thevenin reduces a network to a voltage source in series with a resistance; Norton reduces it to a current source in parallel with a resistance. Either can be converted into the other.

What is a Fourier series used for?

A Fourier series expresses a periodic signal as a sum of sine and cosine components. It allows waveforms to be analysed in terms of their frequency content.