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Equations for time-invariant AC circuits take the same form as Ohm's law. However, the variables are generalized to complex numbers and the current and voltage waveforms are complex exponentials. [29] In this approach, a voltage or current waveform takes the form Ae st, where t is time, s is a complex parameter, and A is a complex scalar.
The current entering any junction is equal to the current leaving that junction. i 2 + i 3 = i 1 + i 4. This law, also called Kirchhoff's first law, or Kirchhoff's junction rule, states that, for any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node; or equivalently:
This equation, along with the continuity equation for J and the Poisson's equation for E, form a set of partial differential equations. In special cases, an exact or approximate solution to these equations can be worked out by hand, but for very accurate answers in complex cases, computer methods like finite element analysis may be required.
Simulation-based methods for time-based network analysis solve a circuit that is posed as an initial value problem (IVP). That is, the values of the components with memories (for example, the voltages on capacitors and currents through inductors) are given at an initial point of time t 0 , and the analysis is done for the time t 0 ≤ t ≤ t f ...
Often, an equivalent circuit is sought that simplifies calculation, and more broadly, that is a simplest form of a more complex circuit in order to aid analysis. [1] In its most common form, an equivalent circuit is made up of linear, passive elements. However, more complex equivalent circuits are used that approximate the nonlinear behavior of ...
When calculating a Thévenin-equivalent voltage, the voltage divider principle is often useful, by declaring one terminal to be V out and the other terminal to be at the ground point. The Thévenin-equivalent resistance R Th is the resistance measured across points A and B "looking back" into the circuit. The resistance is measured after ...
Representation of a lumped model consisting of a voltage source and a resistor. The lumped-element model (also called lumped-parameter model, or lumped-component model) is a simplified representation of a physical system or circuit that assumes all components are concentrated at a single point and their behavior can be described by idealized mathematical models.
The best-known bridge circuit, the Wheatstone bridge, was invented by Samuel Hunter Christie and popularized by Charles Wheatstone, and is used for measuring resistance. It is constructed from four resistors, two of known values R 1 and R 3 (see diagram), one whose resistance is to be determined R x , and one which is variable and calibrated R 2 .
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