Series and parallel circuitsTwo-terminal components and electrical networks can be connected in series or parallel. The resulting electrical network will have two terminals, and itself can participate in a series or parallel topology. Whether a two-terminal "object" is an electrical component (e.g. a resistor) or an electrical network (e.g. resistors in series) is a matter of perspective. This article will use "component" to refer to a two-terminal "object" that participate in the series/parallel networks.
Equivalent circuitIn electrical engineering, an equivalent circuit refers to a theoretical circuit that retains all of the electrical characteristics of a given circuit. Often, an equivalent circuit is sought that simplifies calculation, and more broadly, that is a simplest form of a more complex circuit in order to aid analysis. In its most common form, an equivalent circuit is made up of linear, passive elements. However, more complex equivalent circuits are used that approximate the nonlinear behavior of the original circuit as well.
Kirchhoff's circuit lawsKirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhoff. This generalized the work of Georg Ohm and preceded the work of James Clerk Maxwell. Widely used in electrical engineering, they are also called Kirchhoff's rules or simply Kirchhoff's laws. These laws can be applied in time and frequency domains and form the basis for network analysis.
ResistorA resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active elements, and terminate transmission lines, among other uses. High-power resistors that can dissipate many watts of electrical power as heat may be used as part of motor controls, in power distribution systems, or as test loads for generators.
Direct currentDirect current (DC) is one-directional flow of electric charge. An electrochemical cell is a prime example of DC power. Direct current may flow through a conductor such as a wire, but can also flow through semiconductors, insulators, or even through a vacuum as in electron or ion beams. The electric current flows in a constant direction, distinguishing it from alternating current (AC). A term formerly used for this type of current was galvanic current.
Parallel transportIn geometry, parallel transport (or parallel translation) is a way of transporting geometrical data along smooth curves in a manifold. If the manifold is equipped with an affine connection (a covariant derivative or connection on the tangent bundle), then this connection allows one to transport vectors of the manifold along curves so that they stay parallel with respect to the connection. The parallel transport for a connection thus supplies a way of, in some sense, moving the local geometry of a manifold along a curve: that is, of connecting the geometries of nearby points.
Network analysis (electrical circuits)In electrical engineering and electronics, a network is a collection of interconnected components. Network analysis is the process of finding the voltages across, and the currents through, all network components. There are many techniques for calculating these values; however, for the most part, the techniques assume linear components. Except where stated, the methods described in this article are applicable only to linear network analysis.
Connection (mathematics)In geometry, the notion of a connection makes precise the idea of transporting local geometric objects, such as tangent vectors or tensors in the tangent space, along a curve or family of curves in a parallel and consistent manner. There are various kinds of connections in modern geometry, depending on what sort of data one wants to transport. For instance, an affine connection, the most elementary type of connection, gives a means for parallel transport of tangent vectors on a manifold from one point to another along a curve.
Connection (vector bundle)In mathematics, and especially differential geometry and gauge theory, a connection on a fiber bundle is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. The most common case is that of a linear connection on a vector bundle, for which the notion of parallel transport must be linear. A linear connection is equivalently specified by a covariant derivative, an operator that differentiates sections of the bundle along tangent directions in the base manifold, in such a way that parallel sections have derivative zero.
Alternating currentAlternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time, in contrast to direct current (DC), which flows only in one direction. Alternating current is the form in which electric power is delivered to businesses and residences, and it is the form of electrical energy that consumers typically use when they plug kitchen appliances, televisions, fans and electric lamps into a wall socket. A common source of DC power is a battery cell in a flashlight.
Thévenin's theoremAs originally stated in terms of direct-current resistive circuits only, Thévenin's theorem states that "Any linear electrical network containing only voltage sources, current sources and resistances can be replaced at terminals A–B by an equivalent combination of a voltage source Vth in a series connection with a resistance Rth." The equivalent voltage Vth is the voltage obtained at terminals A–B of the network with terminals A–B open circuited.
Norton's theoremIn direct-current circuit theory, Norton's theorem, also called the Mayer–Norton theorem, is a simplification that can be applied to networks made of linear time-invariant resistances, voltage sources, and current sources. At a pair of terminals of the network, it can be replaced by a current source and a single resistor in parallel. For alternating current (AC) systems the theorem can be applied to reactive impedances as well as resistances. The Norton equivalent circuit is used to represent any network of linear sources and impedances at a given frequency.
Electrical resistance and conductanceThe electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallels with mechanical friction. The SI unit of electrical resistance is the ohm (Ω), while electrical conductance is measured in siemens (S) (formerly called the 'mho' and then represented by ℧). The resistance of an object depends in large part on the material it is made of.
Levi-Civita connectionIn Riemannian or pseudo-Riemannian geometry (in particular the Lorentzian geometry of general relativity), the Levi-Civita connection is the unique affine connection on the tangent bundle of a manifold (i.e. affine connection) that preserves the (pseudo-)Riemannian metric and is torsion-free. The fundamental theorem of Riemannian geometry states that there is a unique connection which satisfies these properties. In the theory of Riemannian and pseudo-Riemannian manifolds the term covariant derivative is often used for the Levi-Civita connection.
Electric currentAn electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. The moving particles are called charge carriers, which may be one of several types of particles, depending on the conductor. In electric circuits the charge carriers are often electrons moving through a wire. In semiconductors they can be electrons or holes.
Connection (principal bundle)In mathematics, and especially differential geometry and gauge theory, a connection is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. A principal G-connection on a principal G-bundle P over a smooth manifold M is a particular type of connection which is compatible with the action of the group G. A principal connection can be viewed as a special case of the notion of an Ehresmann connection, and is sometimes called a principal Ehresmann connection.
RL circuitA resistor–inductor circuit (RL circuit), or RL filter or RL network, is an electric circuit composed of resistors and inductors driven by a voltage or current source. A first-order RL circuit is composed of one resistor and one inductor, either in series driven by a voltage source or in parallel driven by a current source. It is one of the simplest analogue infinite impulse response electronic filters. The fundamental passive linear circuit elements are the resistor (R), capacitor (C) and inductor (L).
Equivalent series resistancePractical capacitors and inductors as used in electric circuits are not ideal components with only capacitance or inductance. However, they can be treated, to a very good degree of approximation, as being ideal capacitors and inductors in series with a resistance; this resistance is defined as the equivalent series resistance (ESR). If not otherwise specified, the ESR is always an AC resistance, which means it is measured at specified frequencies, 100 kHz for switched-mode power supply components, 120 Hz for linear power-supply components, and at its self-resonant frequency for general-application components.
Parallel communicationIn data transmission, parallel communication is a method of conveying multiple binary digits (bits) simultaneously using multiple conductors. This contrasts with serial communication, which conveys only a single bit at a time; this distinction is one way of characterizing a communications link. The basic difference between a parallel and a serial communication channel is the number of electrical conductors used at the physical layer to convey bits. Parallel communication implies more than one such conductor.
VoltageVoltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to move a test charge between the two points. In the International System of Units (SI), the derived unit for voltage is named volt. The voltage between points can be caused by the build-up of electric charge (e.g., a capacitor), and from an electromotive force (e.g.
