A current divider is a parallel connection in which a total current splits between branches in inverse proportion to their resistances. For two branches, I₁ = I_total × R₂/(R₁ + R₂) and I₂ = I_total × R₁/(R₁ + R₂).
Learning objectives
- Apply the two-branch current divider formula.
- Explain why the smaller resistance carries more current.
- Verify branch currents with Kirchhoff’s current law.
- Recognise when source resistance or AC reactance invalidates the simple formula.
Progressive explanation
Start with the plain-language idea, then move into the engineering detail. Each level stands on its own, so you can stop at the depth you need.
Beginner The core idea
This is the opposite of a voltage divider, where the larger resistance takes the larger share of voltage. Current division explains why a short circuit takes most of the current, why parallel lamps share current according to their power ratings, and why adding a low-resistance branch increases the total current.
Intermediate How it behaves in a circuit
For more than two branches, use conductances: Iₙ = I_total × Gₙ/ΣG, where G = 1/R. Kirchhoff’s current law provides the check that the branch currents sum to the total. The formula assumes the total current is fixed; if the source has significant internal resistance, adding or changing a branch changes the total current too.
Advanced Limits, assumptions, engineering detail
Practical current sharing is affected by wire resistance, contact resistance and component tolerance. Precision current shunts and current-sense resistors are chosen with low temperature coefficient because their resistance changes with self-heating. In power electronics, parallel switching devices need balancing networks or active control to share current, because a small difference in on-resistance can cause a large imbalance at high current.
Formulas and variables
Units of measurement
| Quantity | Symbol | Unit |
|---|---|---|
| Current | I | ampere (A) |
| Resistance | R | ohm (Ω) |
| Conductance | G | siemens (S) |
| Voltage | V | volt (V) |
Worked examples
Current split between two resistors
Problem. A total current of 6.0 A enters a parallel pair of 10 Ω and 15 Ω. Find each branch current.
Solution. I₁₀ = 6.0 × 15/(10 + 15) = 90/25 = 3.6 A. I₁₅ = 6.0 × 10/25 = 60/25 = 2.4 A. Check: 3.6 + 2.4 = 6.0 A, and both branches have 3.6 × 10 = 36 V and 2.4 × 15 = 36 V.
Three-way current division using conductances
Problem. A total current of 3.0 A splits between 4 Ω, 12 Ω and 6 Ω in parallel. Find the current in the 4 Ω branch and the 12 Ω branch.
Solution. Conductances: G₁ = 1/4 = 0.25 S, G₂ = 1/12 ≈ 0.0833 S, G₃ = 1/6 ≈ 0.1667 S; ΣG ≈ 0.50 S. I₄ = 3.0 × 0.25/0.50 = 1.5 A. I₁₂ = 3.0 × 0.0833/0.50 = 0.50 A. The remaining 1.0 A flows in the 6 Ω branch. Common voltage: 1.5 × 4 = 0.5 × 12 = 1.0 × 6 = 6.0 V.
Practical applications
- Parallel load current sharing
- Current-sense shunt networks
- Parallel battery and converter branches
- Biasing and signal-splitting networks
Automotive applications
Current division explains why a shorted branch in a vehicle circuit can starve the intended load and blow a fuse: the low-resistance fault takes most of the current. It also helps interpret parallel loads, such as two lamps of different power ratings sharing a supply. When adding accessories, the new parallel branch changes the current distribution and can overload a shared feed.
Industrial applications
Industrial current sharing appears in parallel feeders, parallel battery strings and parallel power converters. Cables and converters are matched and derated to share current evenly; a small resistance difference can cause a significant imbalance at high current. In instrumentation, current dividers are used to extend the range of a current-measuring circuit, but the shunt resistance and its temperature coefficient then determine the accuracy.
Measurement procedure
- Measure the total current and each branch current separately, then verify that the branch currents add to the total.
- Measure the voltage across the parallel group; each branch current should equal V/R for that branch.
- Use a clamp meter on individual conductors; clamping several parallel conductors together reads the net current.
- For low-resistance shunts, use a four-wire measurement to avoid lead resistance affecting the result.
Common mistakes
- Using the voltage divider formula for a current divider.
- Assigning the larger current to the larger resistance.
- Forgetting to verify the branch currents sum to the total current.
- Applying the simple formula when the source resistance is significant and changes the total current.
Safety considerations
- A low-resistance parallel branch can draw a large current and overheat wiring; ensure protection is correctly rated.
- Current-sense shunts can be at a hazardous potential; use isolated measurement equipment.
- Do not open a branch of a current-carrying parallel circuit unless the resulting redistribution is safe and understood.