Current Divider Calculator
Calculate how current divides between two parallel resistors using the current divider rule. Enter the total current and both resistance values to find individual branch currents. See also our Parallel Resistor Calculator and Voltage Divider Calculator.
How to Use the Current Divider Rule
The current divider rule is a fundamental principle in electrical circuit analysis that determines how current splits between parallel branches. When a current source or total current enters a parallel combination of resistors, the current divides inversely proportional to the resistance of each branch — more current flows through the path of least resistance. This is the dual of the voltage divider rule used for series circuits.
To use this calculator, enter the total current flowing into the parallel combination and the resistance values of both branches. The calculator applies the current divider formula to determine how much current flows through each resistor. It also calculates the equivalent parallel resistance and the voltage across the combination, which is the same for both branches since they are in parallel.
The key insight of the current divider is counterintuitive at first: the branch with the larger resistance carries less current, while the branch with smaller resistance carries more current. This makes physical sense because parallel branches share the same voltage, so by Ohm's Law (I = V/R), a smaller resistance produces a larger current for the same voltage.
Current Divider Formula
Two-Resistor Current Divider:
I₁ = I_total × R₂ / (R₁ + R₂)
I₂ = I_total × R₁ / (R₁ + R₂)
General Form (N resistors):
I_k = I_total × (R_total_parallel / R_k)
Parallel Resistance:
R_parallel = (R₁ × R₂) / (R₁ + R₂)
Voltage Across Parallel Combination:
V = I_total × R_parallel
Verification:
I₁ + I₂ = I_total (Kirchhoff's Current Law)
Example Calculation
A 10A current source feeds two parallel resistors: R₁ = 100Ω and R₂ = 200Ω. Find the current through each resistor:
Given: I_total = 10A, R₁ = 100Ω, R₂ = 200Ω
I₁ = 10 × 200/(100+200) = 10 × 200/300 = 6.6667 A
I₂ = 10 × 100/(100+200) = 10 × 100/300 = 3.3333 A
R_parallel = (100 × 200)/(100+200) = 20000/300 = 66.6667 Ω
V = 10 × 66.6667 = 666.667 V
Verify: I₁ + I₂ = 6.6667 + 3.3333 = 10.0000 A ✓
Verify: I₁ = V/R₁ = 666.667/100 = 6.6667 A ✓
Notice that R₁ (100Ω) carries twice the current of R₂ (200Ω) because it has half the resistance. The smaller resistor always carries the larger share of current in a parallel circuit. This principle is used extensively in current sensing, load sharing, and biasing circuits.
Current Divider Reference Table
| I_total (A) | R₁ (Ω) | R₂ (Ω) | I₁ (A) | I₂ (A) |
|---|---|---|---|---|
| 1 A | 100 Ω | 100 Ω | 0.5000 A | 0.5000 A |
| 2 A | 100 Ω | 200 Ω | 1.3333 A | 0.6667 A |
| 5 A | 50 Ω | 100 Ω | 3.3333 A | 1.6667 A |
| 10 A | 100 Ω | 200 Ω | 6.6667 A | 3.3333 A |
| 10 A | 100 Ω | 300 Ω | 7.5000 A | 2.5000 A |
| 10 A | 200 Ω | 200 Ω | 5.0000 A | 5.0000 A |
| 10 A | 1000 Ω | 1000 Ω | 5.0000 A | 5.0000 A |
| 15 A | 47 Ω | 100 Ω | 10.2041 A | 4.7959 A |
| 20 A | 10 Ω | 30 Ω | 15.0000 A | 5.0000 A |
| 20 A | 100 Ω | 400 Ω | 16.0000 A | 4.0000 A |
| 50 A | 220 Ω | 330 Ω | 30.0000 A | 20.0000 A |
| 100 A | 10 Ω | 10 Ω | 50.0000 A | 50.0000 A |
Frequently Asked Questions
What is the current divider rule?
The current divider rule states that in a parallel circuit, the current through any branch is equal to the total current multiplied by the ratio of the opposite branch resistance to the sum of all resistances. For two resistors: I₁ = I_total × R₂/(R₁+R₂). Current divides inversely proportional to resistance — lower resistance carries more current.
How is the current divider different from the voltage divider?
The voltage divider applies to series circuits where voltage divides proportionally to resistance (higher R gets more voltage). The current divider applies to parallel circuits where current divides inversely to resistance (lower R gets more current). They are mathematical duals of each other. Voltage dividers use the same resistor in the formula, while current dividers use the opposite resistor.
Can the current divider be used with more than two resistors?
Yes. For N parallel resistors, the current through resistor k is: I_k = I_total × (R_eq / R_k), where R_eq is the total equivalent parallel resistance of all N resistors. This generalizes the two-resistor formula. You can also repeatedly apply the two-resistor formula by combining resistors in stages.
Why does the smaller resistor carry more current?
In a parallel circuit, all branches have the same voltage across them. By Ohm's Law (I = V/R), a smaller resistance produces a larger current for the same voltage. Think of it like water flowing through pipes — a wider pipe (lower resistance) allows more water (current) to flow for the same pressure (voltage).
What happens when both resistors are equal?
When R₁ = R₂, the current divides equally between both branches: I₁ = I₂ = I_total/2. This is the simplest case and is often used in current mirror circuits, balanced loads, and symmetrical designs. For N equal resistors in parallel, each carries I_total/N.
What are practical applications of the current divider?
Current dividers are used in ammeter shunt resistors (extending meter range), current sensing circuits, LED arrays with parallel strings, load sharing between parallel power supplies, transistor biasing networks, and current mirrors in analog IC design. Understanding current division is essential for any parallel circuit analysis.
Current Divider in Circuit Analysis
The current divider rule is one of the most frequently used shortcuts in circuit analysis, alongside the voltage divider rule and Kirchhoff's laws. It allows you to quickly determine branch currents without first calculating the voltage across the parallel combination. In complex circuits, you can often simplify sections into parallel combinations and apply the current divider rule to find individual branch currents efficiently.
When analyzing circuits with current sources, the current divider is particularly useful because the total current is already known. For circuits with voltage sources, you typically first find the total current using Ohm's Law with the equivalent resistance, then apply the current divider to find individual branch currents. This two-step approach is faster than solving simultaneous equations for most practical circuits.
Ammeter Shunt Resistor Design
One of the most important applications of the current divider is designing ammeter shunt resistors. A shunt is a low-value resistor placed in parallel with a galvanometer to extend its current range. If the galvanometer has internal resistance R_g and full-scale deflection current I_g, and you want to measure a maximum current I_max, the shunt resistance is: R_shunt = (I_g × R_g) / (I_max - I_g). The current divider ensures most of the current bypasses the sensitive meter movement through the low-resistance shunt.