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These include resistors in series, resistors in parallel and the extension to series and parallel circuits for capacitors, inductors and general impedances. Also well known are the Norton and Thévenin equivalent current generator and voltage generator circuits respectively, as is the Y-Δ transform. None of these are discussed in detail here ...
Another equivalent version is a single charged capacitor short circuited by a perfect conductor. In these cases in the final state the entire charge has been neutralized, the final voltage on the capacitors is zero, so the entire initial energy has vanished. The solutions to where the energy went are similar to those described in the previous ...
Components connected in parallel are connected along multiple paths, and each component has the same voltage across it, equal to the voltage across the network. The current through the network is equal to the sum of the currents through each component. The two preceding statements are equivalent, except for exchanging the role of voltage and ...
Leakage is equivalent to a resistor in parallel with the capacitor. Constant exposure to factors such as heat, mechanical stress, or humidity can cause the dielectric to deteriorate resulting in excessive leakage, a problem often seen in older vacuum tube circuits, particularly where oiled paper and foil capacitors were used.
Source transformations are easy to compute using Ohm's law.If there is a voltage source in series with an impedance, it is possible to find the value of the equivalent current source in parallel with the impedance by dividing the value of the voltage source by the value of the impedance.
A common form is a parallel-plate capacitor, which consists of two conductive plates insulated from each other, usually sandwiching a dielectric material. In a parallel plate capacitor, capacitance is very nearly proportional to the surface area of the conductor plates and inversely proportional to the separation distance between the plates.
The op-amp inverting amplifier is a typical circuit, with parallel negative feedback, based on the Miller theorem, where the op-amp differential input impedance is apparently decreased to zero Zeroed impedance uses an inverting (usually op-amp) amplifier with enormously high gain A v → ∞ {\displaystyle A_{v}\to \infty } .
The equivalent capacitance is called electrochemical capacitance ¯ = +. Quantum capacitance is especially important for low-density-of-states systems, such as a 2-dimensional electronic system in a semiconductor surface or interface or graphene , and can be used to construct an experimental energy functional of electron density.
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