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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]
The following formulae use it, assuming a constant voltage applied across the capacitor and resistor in series, to determine the voltage across the capacitor against time: Charging toward applied voltage (initially zero voltage across capacitor, constant V 0 across resistor and capacitor together) V 0 : V ( t ) = V 0 ( 1 − e − t / τ ...
A resistor–capacitor circuit (RC circuit), or RC filter or RC network, is an electric circuit composed of resistors and capacitors. It may be driven by a voltage or current source and these will produce different responses. A first order RC circuit is composed of one resistor and one capacitor and is the simplest type of RC circuit.
The resonant frequency is defined as the frequency at which the impedance of the circuit is at a minimum. Equivalently, it can be defined as the frequency at which the impedance is purely real (that is, purely resistive). This occurs because the impedances of the inductor and capacitor at resonant are equal but of opposite sign and cancel out.
It is common for electrical components to have slightly reduced capacitances at extreme frequencies, due to slight inductance of the internal conductors used to make capacitors (not just the leads), and permittivity changes in insulating materials with frequency: C is very nearly, but not quite a constant.
Miller's theorem can be used to effect this replacement: it states that, if the gain ratio of two nodes is 1 / K , then an impedance of Z connecting the two nodes can be replaced with a Z / 1 − K impedance between the first node and ground and a KZ / K − 1 impedance between the second node and ground.
The reactance and impedance of a capacitor are respectively = = = = = where j is the imaginary unit and ω is the angular frequency of the sinusoidal signal. The − j phase indicates that the AC voltage V = ZI lags the AC current by 90°: the positive current phase corresponds to increasing voltage as the capacitor charges; zero current ...
In electronics, a constant phase element is an equivalent electrical circuit component that models the behaviour of a double layer, that is, an imperfect capacitor (see double-layer capacitance). Constant phase elements are also used in equivalent circuit modeling and data fitting of electrochemical impedance spectroscopy data.