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

在并联电路中，电阻器连接在相同的两个节点之间，使得每个电阻器两端的电压相等。根据电路示意图并应用基尔霍夫电流定律，通过这些电阻的电流之和等于电源电流。根据欧姆定律，电源电流等于电源电压乘以各个电阻倒数之和。求解电源电压并将其代入欧姆定律，可得到流经每个电阻的电流。在电流分流电路中，流经各电阻的电流与其电阻值成反比分配，体现了电流分流的原理。对于并联电阻的组合，其等效电阻的倒数等于各个电阻倒数之和。电导是电阻的倒数，可以分别计算串联和并联电路的电导。串联时，等效电导等于各电导的乘积除以它们的和；而并联时，等效电导等于各电导之和。

电流分频器

Current Dividers

在并联电气连接中，电阻器会连接在同一对节点之间，从而在每个电阻器上产生相等的电压。基尔霍夫电流定律会应用这些连接，并以此来确定流经这些电阻器的电流总和是否等于源电流。通过欧姆定律可以得知，源电流能够被确定为源电压与各个电阻的倒数之和的乘积。这种关系简化了查找流经每个电阻器中电流的过程。 在并联电路中，源电流能够以与其电阻成反比的方式在电阻器之间进行分配，这体现了分流器电路中的“电流分配”原理。 并联电阻器可以视为单个等效电阻器，从而简化了电路的复杂性。等效电阻器的值能够计算为各个电阻除以它们的总和的乘积。其中两个并联的电阻器能够通过将它们的电阻进行相乘并除以它们的总和来产生等效电阻。这一概念能够扩展到具有两个以上并联电阻的电路，并使用类似的方法来确定等效电阻。 <img alt="Equation1" src="/files/ftp_upload/15073/15073_PT_Equation_1.svg" style="text-align: center; height: 36px;"> 电导是电阻的倒数，是串联和并联连电路中的一个重要参数。在串联的电阻器中，等效电导是由各个电导除以它们的总和的乘积所得出的。相反，在并联的配置中，它能够代表各个电导的总和。电导的使用为计算并联电阻器提供了便利。并联电阻器中的等效电导等于其各自电导的总和，从而能够计算出串联电阻器中的等效电阻。 在实际场景中，串联和并联配置的电阻器组合有助于其能够简化复杂的网络。这种简化有助于电路的分析和设计，同时在简化的过程中还能够保留原始网络中的电流-电压 (i-v) 特性。

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

charge and current

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ohm's law

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kirchhoff's current law

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current dividers

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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key terms and concepts

Learn how current divides in parallel resistors, how to find equivalent resistance, and why conductance simplifies circuit analysis for high school students.

Parallel Resistors and Current Division | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Parallel Resistors and Current Division

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