Current Divider Calculator
Analyze current distribution in parallel circuits.
Circuit Parameters
Individual Resistance Values ($R_1, R_2, …$, Ohms)
The Current Divider Rule
The Current Divider Rule (CDR) is a fundamental theorem in electrical engineering used to determine how the total current entering a parallel network is split among the individual branches. This rule is crucial for analyzing complex circuits, especially those involving multiple parallel components. [Image of current divider circuit]
Formula Implementation
For a network of $N$ parallel resistors, the current $I_x$ flowing through any branch $R_x$ is given by the general formula:
$$I_x = I_{total} \cdot \frac{R_{eq}}{R_x}$$
Where $I_{total}$ is the total current entering the network, $R_x$ is the resistance of the branch, and $R_{eq}$ is the equivalent resistance of the entire parallel network. $R_{eq}$ is calculated as:
$$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_n}$$
Two-Resistor Case
When only two resistors ($R_1$ and $R_2$) are in parallel, the formula simplifies to the reciprocal relationship, which is often easier to apply:
$$I_1 = I_{total} \cdot \frac{R_2}{R_1 + R_2}$$
$$I_2 = I_{total} \cdot \frac{R_1}{R_1 + R_2}$$
Practical Applications
- Circuit Design: Ensuring sensitive components (like LEDs or microcontrollers) receive the correct operating current by diverting excess current through parallel branches.
- Fault Analysis: Quickly estimating current changes when a component fails or is added in a parallel network.
- Meter Shunts: Designing ammeter shunts (low-resistance parallel resistors) to extend the measurement range of the meter by diverting most of the current away from the galvanometer.
How to Use This Tool
- Enter Total Current ($I_{total}$): Input the total current (in Amperes) that enters the junction of the parallel network.
- Set Number of Resistors ($N$): Specify how many resistors are connected in parallel (minimum of 2, maximum of 10). Changing this number will dynamically update the resistance input fields below.
- Input Resistances ($R_n$): Enter the positive resistance value (in Ohms) for each individual resistor ($R_1, R_2, …$).
- Calculate: Click the “Calculate Branch Currents” button.
- View Results: The tool will display the calculated Equivalent Resistance ($R_{eq}$) and the individual current ($I_x$) flowing through each resistor, rounded to two decimal places.
