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Capacitance and RC Circuits Capacitors are constructed by separating 2 sheets of conductor, which is usually metallic, by a thin layer of insulating material. In parallel-plate capacitor, the sheets are flat and parallel. The insulating material between the plates, called a dielectric, can be air, Mylar, polyester, polypropylene, mica, etc. Stored charge in terms of voltage q Cv The constant of proportionality is the capacitance C, which has units of farads (F). Farads are equivalent to coulombs per volt. Current in terms of voltage dq d i (Cv) dt dt Cdv i dt Note: the current reference direction points into the positive reference polarity. Voltage in terms of current Suppose that we know the current i(t) flowing through a capacitance C and we want to compute charge and voltage. t q(t ) i (t )dt q (t0 ) t0 q(t0 ) 1 t v(t ) i (t )dt C t0 C 1 t v(t ) i (t )dt v(t0 ) C t0 Stored Energy Energy stored in the capacitance is given by 1 2 w(t ) Cv (t ) 2 1 w(t ) v(t )q(t ) 2 q 2 (t ) w(t ) 2C Capacitance of the parallel-plate capacitor If the distance d between the plates is much smaller than both the width and the length of the plates, the capacitance is approximately C A d In which is the dielectric constant of the material between the plates. For vacuum, the dielectric constant is 0 8.85x10-12 F/m Inductance An inductor is constructed by coiling a wire around some type of form. Current flowing through the coil creates a magnetic field or flux that links the coil. Frequently the coil form is composed of a magnetic material such as iron or iron oxide that increases the magnetic flux for a given current. When the current changes in value, the resulting magnetic flux changes according to Faraday’s law of electromagnetic induction, time-varying magnetic flux linking a coil induces voltage across the coil. For an ideal inductor, the voltage is proportional to the time rate of change of the current. Furthermore, the polarity of the voltage is such as to oppose the change in current. The constant of proportionality is called inductance, L. di v(t ) L dt Current in terms of voltage di v(t ) L dt 1 di v(t )dt L i (t ) 1 t i (t0 )di L t0 v(t )dt 1 t i (t ) v(t )dt i (t0 ) L t0 Stored Energy 1 2 w(t ) Li (t ) 2