Table of Contents
Current Divider Rule
The current divider rule describes how electric current splits between parallel branches in a circuit. Current prefers the path of least resistance: more current flows through the lower resistance branch. The current through each branch is inversely proportional to its resistance relative to the total parallel resistance. This rule is the dual of the voltage divider rule, which applies to series resistors.
The current divider is a fundamental circuit analysis technique used in electronics, power distribution, and sensor circuits. Understanding how current divides is essential for designing parallel circuits, analyzing fault currents, sizing conductors, and building current-sensing circuits. The principle extends to any parallel impedance network, including those with capacitors and inductors in AC circuits.
Formula
Examples
| Itotal | R1 | R2 | I1 | I2 |
|---|---|---|---|---|
| 10 A | 100 Ω | 100 Ω | 5 A | 5 A |
| 10 A | 100 Ω | 200 Ω | 6.67 A | 3.33 A |
| 5 A | 10 Ω | 40 Ω | 4 A | 1 A |
| 1 A | 1k Ω | 3k Ω | 0.75 A | 0.25 A |
Applications
- Current sensing: a low-value shunt resistor in parallel with a higher resistance creates a known current division for measurement.
- Power distribution: parallel feeders in electrical systems divide load current based on cable impedance.
- LED arrays: parallel LED strings with ballast resistors divide current for uniform brightness.
- Transistor biasing: current mirrors and bias networks use current division principles extensively.
Frequently Asked Questions
Why does more current flow through the lower resistance?
In a parallel circuit, all branches have the same voltage across them. By Ohm's law (I = V/R), a lower resistance with the same voltage produces a higher current. The total current divides in inverse proportion to the resistances, with the lower resistance branch carrying more current. This is the opposite of series circuits, where resistors share the same current.
Does the current divider work for more than two resistors?
Yes, but the formula becomes different. For n parallel resistors, the current through resistor Rk is: Ik = Itotal × (Req/Rk), where Req is the equivalent parallel resistance of all n resistors. For two resistors, this simplifies to the familiar R2/(R1+R2) form used in this calculator.
How does temperature affect current division?
If the resistors have different temperature coefficients, their resistances change unequally with temperature, altering the current division ratio. This is important in power circuits where resistors heat up during operation. Wire-wound and metal film resistors have lower temperature coefficients than carbon resistors, providing more stable current division over temperature.