1.11: Current Dividers
In parallel electrical connections, resistors are linked between the same pair of nodes, creating an equal voltage across each resistor. Kirchhoff's current law is applied to these connections, establishing that the sum of currents through these resistors equals the source current. Utilizing Ohm's law, the source current is determined as the product of the source voltage and the sum of the reciprocals of individual resistances. This relationship simplifies the process of finding the current flowing through each resistor.
In a parallel arrangement, the source current distributes itself among the resistors in inverse proportion to their resistances, exemplifying the "current division" principle within a current divider circuit.
Parallel resistors can be approached as a single equivalent resistor, simplifying circuit complexity. The equivalent resistor's value is calculated as the product of individual resistances divided by their sum. Two parallel resistors yield an equivalent resistance by multiplying their resistances and dividing by their sum. This concept extends to circuits featuring more than two resistors in parallel, with the equivalent resistance determined using a similar approach.
Conductance, the reciprocal of resistance, is a valuable parameter in series and parallel connections. In series resistors, the equivalent conductance stems from the product of individual conductances divided by their sum. Conversely, in parallel configurations, it represents the sum of the individual conductances. The use of conductance calculations offers convenience when handling parallel resistors. The equivalent conductance of parallel resistors becomes the sum of their individual conductances, mirroring the equivalent resistance calculation for series resistors.
In practical scenarios, the combination of resistors in both series and parallel configurations aids in simplifying complex networks. This simplification facilitates the analysis and design of electrical circuits while preserving the original network's current-voltage (i-v) characteristics within the simplified setup.
