Name: parallel resistors and current division
Uploaded: 2025-04-15T13:26:50.000Z
Duration: 1 min 10 s
Channel: JoVE

In a parallel connection, resistors are connected between the same pair of nodes, creating an equal voltage across each.Considering the schematic circuit and applying Kirchhoff's current law, the sum of the currents through these resistors equals the source current.Using Ohm's law, the source current equals the source voltage multiplied by the sum of the reciprocals of the individual resistances.Solving for the source voltage and substituting it into Ohm's law gives the current passing through each resistor.The source current is divided among the resistors in an inverse proportion to their resistances, demonstrating the principle of current division in a current divider circuit.For a combination of parallel resistors, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances.Conductance, the inverse of resistance, can be calculated for series and parallel connections.In series, the equivalent conductance is the product of the individual conductances divided by their sum, while in parallel, it is the sum of the individual conductances.

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.
<img alt="Parallel resistance formula; equation for calculating equivalent resistance in parallel circuits." src="/files/ftp_upload/15073/15073_PT_Equation_1.svg" style="text-align: center; height: 36px;" data-altupdatedat="1761848533000" data-alt="Equation1" />
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.

Current Dividers

In a parallel connection, resistors are connected between the same pair of nodes, creating an equal voltage across each.
Considering the schematic circuit ...

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parallel resistors and current division

Parallel resistors share the same two nodes, so each resistor has the same voltage across it. In this circuit setup, Kirchhoff's current law applies. The source current equals the sum of the currents through each branch.

Ohm's law helps find the branch currents from the source voltage and the resistor values. The source current is equal to the source voltage times the sum of the reciprocals of the resistances. This makes it easier to calculate how current divides in the circuit. The current splits in inverse proportion to resistance, which is the current division principle.

Parallel resistors can also be replaced by one equivalent resistor. This step reduces circuit complexity while keeping the same current-voltage behavior. For two resistors in parallel, the equivalent resistance is found by multiplying the resistances and dividing by their sum. The same idea can be used for more than two parallel resistors.

Conductance, which is the reciprocal of resistance, is also useful in circuit analysis. For series resistors, equivalent conductance comes from the product of the individual conductances divided by their sum. For parallel resistors, equivalent conductance is the sum of the individual conductances. Using conductance can make calculations with parallel circuits more convenient, especially when simplifying mixed series and parallel networks.

Parallel Resistors and Current Division

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Parallel resistors share the same two nodes, so each resistor has the same voltage across it. In this circuit setup, Kirchhoff's current law applies. The source current equals the sum of the currents through each branch. Ohm's law helps find the branch currents from the source voltage and the resistor values. The source current is equal to the source voltage times the sum of the reciprocals of the resistances. This makes it easier to calculate how current divides in the circuit. The current...

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Parallel Resistors and Current Division

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