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In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of resistance and reactance in a circuit. [1]Quantitatively, the impedance of a two-terminal circuit element is the ratio of the complex representation of the sinusoidal voltage between its terminals, to the complex representation of the current flowing through it. [2]
A schematic representation of long distance electric power transmission. From left to right: G=generator, U=step-up transformer, V=voltage at beginning of transmission line, Pt=power entering transmission line, I=current in wires, R=total resistance in wires, Pw=power lost in transmission line, Pe=power reaching the end of the transmission line, D=step-down transformer, C=consumers.
In circuit theory terms, the theorem allows any one-port network to be reduced to a single voltage source and a single impedance. The theorem also applies to frequency domain AC circuits consisting of reactive (inductive and capacitive) and resistive impedances. It means the theorem applies for AC in an exactly same way to DC except that ...
The input impedance of an infinite line is equal to the characteristic impedance since the transmitted wave is never reflected back from the end. Equivalently: The characteristic impedance of a line is that impedance which, when terminating an arbitrary length of line at its output, produces an input impedance of equal value. This is so because ...
Analogous to Ohm's law for direct-current circuits, electrical impedance may be expressed by the formula E = I Z. So, the voltage drop in an AC circuit is the product of the current and the impedance of the circuit.
For a circuit to be modelled with an ideal source, output impedance, and input impedance; the circuit's input reactance can be sized to be the negative of the output reactance at the source. In this scenario, the reactive component of the input impedance cancels the reactive component of the output impedance at the source.
The formula describing a current divider is similar in form to that for the voltage divider. However, the ratio describing current division places the impedance of the considered branches in the denominator, unlike voltage division, where the considered impedance is in the numerator. This is because in current dividers, total energy expended is ...
The theorem can be extended to alternating current circuits that include reactance, and states that maximum power transfer occurs when the load impedance is equal to the complex conjugate of the source impedance. The mathematics of the theorem also applies to other physical interactions, such as: [2] [3] mechanical collisions between two objects,