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One way to deal with these inherent resistances in circuit analysis is to use a lumped-element model to express each physical component as a combination of an ideal component and a small resistor in series, the ESR. The ESR can be measured and included in a component's datasheet. To some extent it can be calculated from the device properties. [2]
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.
Series circuits were formerly used for lighting in electric multiple units trains. For example, if the supply voltage was 600 volts there might be eight 70-volt bulbs in series (total 560 volts) plus a resistor to drop the remaining 40 volts. Series circuits for train lighting were superseded, first by motor-generators, then by solid state devices.
One-element networks are trivial and two-element, [note 3] two-terminal networks are either two elements in series or two elements in parallel, also trivial. The smallest number of elements that is non-trivial is three, and there are two 2-element-kind non-trivial transformations possible, one being both the reverse transformation and the topological dual, of the other.
A voltage drop occurs across each resistor in the network causing each successive "rung" of the ladder (each node of the circuit) to have a higher voltage than the previous one. Since the ladder is a series circuit, the current is the same throughout, and is given by the total voltage divided by the total series resistance (V/R eq).
A typical ESR Meter. This one also measures capacitance. An ESR meter is a two-terminal electronic measuring instrument designed and used primarily to measure the equivalent series resistance (ESR) of real capacitors; usually without the need to disconnect the capacitor from the circuit it is connected to.
Figure 2: 4-bit linear R–2R DAC using unequal resistors. It is not necessary that each "rung" of the R–2R ladder use the same resistor values. It is only necessary that the "2R" value matches the sum of the "R" value plus the Thévenin-equivalent resistance of the lower-significance rungs. Figure 2 shows a linear 4-bit DAC with unequal ...
Randles circuit schematic. In electrochemistry, a Randles circuit is an equivalent electrical circuit that consists of an active electrolyte resistance R S in series with the parallel combination of the double-layer capacitance C dl and an impedance (Z w) of a faradaic reaction.