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In the low-frequency limit, the voltage drop around any loop is zero. This includes imaginary loops arranged arbitrarily in space – not limited to the loops delineated by the circuit elements and conductors. In the low-frequency limit, this is a corollary of Faraday's law of induction (which is one of Maxwell's equations).
Low-Q circuits are therefore damped and lossy and high-Q circuits are underdamped and prone to amplitude extremes if driven at the resonant frequency. [a] Q is related to bandwidth; low-Q circuits are wide-band and high-Q circuits are narrow-band. In fact, it happens that Q is the inverse of fractional bandwidth
The main cause for the appearance of low frequency electromagnetic interferences in home and industrial electric systems is the dense integration of power electronics switching frequency. [2] In time, switching power devices, such as transistors, became cheap, small and easy to use, invading all facets of human activity.
Ohm's law, in the form above, is an extremely useful equation in the field of electrical/electronic engineering because it describes how voltage, current and resistance are interrelated on a "macroscopic" level, that is, commonly, as circuit elements in an electrical circuit.
Both the law of squares and the differential retardation associated with it can be explained with reference to dispersion. This is the phenomenon whereby different frequency components of the telegraph pulse travel down the cable at different speeds depending on the cable materials and geometry. [21]
Thus, the circuit behaves as a low-pass filter. If, though, the output is taken across the resistor, high frequencies are passed and low frequencies are attenuated (since the capacitor blocks the signal as its frequency approaches 0). In this configuration, the circuit behaves as a high-pass filter.
Figure 1: Simple RC circuit and auxiliary circuits to find time constants. Figure 1 shows a simple RC low-pass filter. Its transfer function is found using Kirchhoff's current law as follows. At the output, = , where V 1 is the voltage at the top of capacitor C 1. At the center node:
The frequency at which this equality holds for the particular circuit is called the resonant frequency. The resonant frequency of the LC circuit is =, where L is the inductance in henries, and C is the capacitance in farads. The angular frequency ω 0 has units of radians per second.