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where resistance in ohms and capacitance in farads yields the time constant in seconds or the cutoff frequency in hertz (Hz). The cutoff frequency when expressed as an angular frequency ( ω c = 2 π f c ) {\displaystyle (\omega _{c}{=}2\pi f_{c})} is simply the reciprocal of the time constant.
Wien's bridge is used for precision measurement of capacitance in terms of resistance and frequency. [3] It was also used to measure audio frequencies. The Wien bridge does not require equal values of R or C. At some frequency, the reactance of the series R 2 –C 2 arm will be an exact multiple of the shunt R x –C x arm.
In general, capacitance is a function of frequency. At high frequencies, capacitance approaches a constant value, equal to "geometric" capacitance, determined by the terminals' geometry and dielectric content in the device. A paper by Steven Laux [27] presents a review of numerical techniques for capacitance calculation.
The complex impedance, Z C (in ohms) of a capacitor with capacitance C (in farads) is = The complex frequency s is, in general, a complex number, = +, where j represents the imaginary unit: j 2 = −1, σ is the exponential decay constant (in nepers per second), and
The resistance across the membrane is a function of the number of open ion channels and the capacitance is a function of the properties of the lipid bilayer. The time constant is used to describe the rise and fall of membrane voltage, where the rise is described by V ( t ) = V max ( 1 − e − t / τ ) {\displaystyle V(t)=V_{\textrm {max ...
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].
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 .
This is in contrast to R m (in Ω·m 2) and C m (in F/m 2), which represent the specific resistance and capacitance respectively of one unit area of membrane (in m 2). Thus, if the radius, a , of the axon is known, [ b ] then its circumference is 2 πa , and its r m , and its c m values can be calculated as: