Hong Life CalculatorsUnderstanding the current divider calculator — concept and principle
When a current reaches two resistors connected in parallel, it splits between them. This calculator shows how much of a known total current flows through each branch. It is used to check the load on each resistor, to design shunts that carry most of the current around a meter, and to analyse parallel paths in a larger circuit.
How it is calculated
- Current through R1: I₁ = I · R2 / (R1 + R2)
- Current through R2: I₂ = I · R1 / (R1 + R2)
I is the total current in amperes; R1 and R2 are in ohms. Note the cross-over: the current in one branch depends on the resistance of the other branch. The two branch currents always add up to I.
The principle
Both resistors in parallel share the same voltage, V = I₁R1 = I₂R2. The total current is I = I₁ + I₂ (Kirchhoff's current law). The equivalent resistance of the pair is R1R2 / (R1 + R2), so the common voltage is V = I · R1R2 / (R1 + R2). Dividing that voltage by R1 gives I₁ = I · R2 / (R1 + R2). In words: current takes the easier path in proportion to its conductance, so the smaller resistance carries the larger share. This is the mirror image of the voltage divider, where the larger resistance takes the larger share of voltage.
Worked example
- Inputs: I = 2 A, R1 = 10 Ω, R2 = 30 Ω.
- Sum R1 + R2 = 40 Ω.
- I₁ = 2 × 30 / 40 = 1.5 A.
- I₂ = 2 × 10 / 40 = 0.5 A.
- Check: 1.5 + 0.5 = 2 A, and the voltage is the same on both, 1.5 × 10 = 0.5 × 30 = 15 V.
| Total current (A) | I through R1 (A) |
|---|---|
| 0.5 | 0.375 |
| 1 | 0.75 |
| 1.5 | 1.125 |
| 2 | 1.5 |
| 2.5 | 1.875 |
| 3 | 2.25 |
| 4 | 3 |
How to read the result
The ratio of branch currents is the inverse ratio of resistances: R2 is three times R1, so R1 carries three times the current. Use the branch currents to find each resistor's power, P = I²R: here 1.5² × 10 = 22.5 W in R1 and 0.5² × 30 = 7.5 W in R2. For more than two branches, use conductances: Iₖ = I · Gₖ / ΣG, where G = 1/R.
Common mistakes
- Putting the branch's own resistance in the numerator, which gives the currents the wrong way round.
- Using the two-resistor formula for three or more branches.
- Applying the divider when the total current is not fixed; if the source is a voltage source, find the voltage first and divide by each resistance.
Frequently asked questions
How do I design an ammeter shunt?
Choose the shunt so that it carries I − I_meter while the meter carries its full-scale current: R_shunt = R_meter · I_meter / (I − I_meter).
What if one branch is a short circuit?
Almost all the current goes through the short, and the other branch carries nearly none.
Does the current divider rule work with AC impedances?
Yes, using complex impedances in place of resistances; the result then has both magnitude and phase.
Sources: J. W. Nilsson and S. A. Riedel, Electric Circuits, Pearson · C. K. Alexander and M. N. O. Sadiku, Fundamentals of Electric Circuits, McGraw-Hill