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A circuit is a network that has a closed loop i.e. a return path. A network is a connection of 2 or more simple circuit elements, and may not be a circuit.

The goal when designing electrical networks for signal processing is to apply a predefined operation on potential differences (measured in volts) or currents (measured in amperes). Typical functions for these electrical networks are amplification, oscillation and analog linear algorithmic operations such as additionAddition is one of the basic operations of arithmetic. In its simplest form, addition combines two numbers terms summands , the augend and addend into a single number, the sum . Adding more numbers corresponds to repeated addition. By extension, addition, subtractionIn mathematics, subtraction is one of the four basic arithmetic operations. It is usually denoted by an infix minus sign. The traditional names for the terms of the subtraction c − b a are difference a , minuend (c) and subtrahend (b). Basic subtrac, multiplicationArithmetic In its simplest form, multiplication is a quick way of adding identical numbers. The result of multiplying numbers is called a product''. The numbers being multiplied are called coefficients or factors and individually as the multiplicand and m, divisionThis article is about the arithmetic operation. For other uses, see Division (disambiguation). In mathematics, especially elementary arithmetic, division is an arithmetic operation which is the reverse operation of multiplication and sometimes can be inte, differentiationCalculus In mathematics, the derivative of a function is one of the two central concepts of calculus. The inverse of a derivative is called the antiderivative, or indefinite integral. The derivative of a function at a certain point is a measure of the rat and integrationThis article deals with the concept of an integral in mathematical calculus. For other meanings of "integral" see integration. In calculus, the integral of a function is a generalization of area, mass, volume, sum, and total. Unlike the process of differe.

In the case of power distribution networks, engineers design the circuit to transport the energy as efficiently as possible while at the same time taking into account economic factors, network safety and redundancy. These networks use components such as power lines, cables, circuit breakers, switches and transformers.

To design any electrical circuits, electrical engineers need to be able to predict the voltages and currents in the circuit. Linear circuits can be analysed to a certain extent by hand because complex number theory gives engineers the ability to treat all linear elements using a single mathematical representation.

A number of electrical laws apply to all electrical networks. These include

• Kirchhoff's current law: the sum of all currents entering a node is equal to the sum of all currents leaving the node.
• Kirchhoff's voltage law: the directed sum of the electrical potential differences around a circuit must be zero.
• Ohm's law: the voltage across a resistor is the product of its resistance and the current flowing through it.
• the Y-delta transform
• Norton's theorem: any two-terminal collection of voltage sources and resistors is electrically equivalent to an ideal current source in parallel with a single resistor.
• Thevenin's theorem: any two-terminal combination of voltage sources and resistors is electrically equivalent to a single voltage source in series with a single resistor.
• Millman's method: the voltage on the ends of branches in parallel is equal to the sum of the currents flowing in every branch divided by the total equivalent conductance.

• See also Analysis of resistive circuits.

Other more complex laws may be needed if the network contains nonlinear or reactive components. Non-linear self-regenerative hetrodyning systems can be approximated. Applying these laws results in a set of simultaneous equations that can be solved either by hand or by a computer.