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Series RC circuit. The RC time constant, denoted τ (lowercase tau), the time constant (in seconds) of a resistor–capacitor circuit (RC circuit), is equal to the product of the circuit resistance (in ohms) and the circuit capacitance (in farads):
where C is the capacitance of the capacitor. Solving this equation for V yields the formula for exponential decay: =, where V 0 is the capacitor voltage at time t = 0. The time required for the voltage to fall to V 0 / e is called the RC time constant and is given by, [1]
where L, R and C represent inductance, resistance, and capacitance respectively and s is the complex frequency operator = +. This is the conventional way of representing a general impedance but for the purposes of this article it is mathematically more convenient to deal with elastance , D , the inverse of capacitance, C .
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) [1].
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]
Capacitance is proportional to the area of overlap and inversely proportional to the separation between conducting sheets. The closer the sheets are to each other, the greater the capacitance. An example is the capacitance of a capacitor constructed of two parallel plates both of area separated by a distance .
Reactance is defined as the imaginary part of electrical impedance, and is analogous to but not generally equal to the negative reciprocal of the susceptance – that is their reciprocals are equal and opposite only in the special case where the real parts vanish (either zero resistance or zero conductance). In the special case of entirely zero ...
An LCR meter is a type of electronic test equipment used to measure the inductance (L), capacitance (C), and resistance (R) of an electronic component. [1] In the simpler versions of this instrument the impedance was measured internally and converted for display to the corresponding capacitance or inductance value.
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