Current Divider Calculator (Parallel Branch Currents)

What is a current divider?

A current entering a set of parallel branches splits in inverse proportion to the branch resistances. The branch with the lower resistance takes the larger share. The relation that gives each share is the current divider rule.

Formula

Every branch has the same voltage across it: V = I_T × R_T, where R_T is the parallel equivalent of the branches. Each branch current is that voltage divided by the branch resistance:

I_k = I_T × R_T / R_k

With only two branches there is a shortcut: I1 = I_T × R2 / (R1 + R2). Note that the numerator holds the resistance of the other branch.

Example

A total of 9 A enters two branches of 6 Ω and 3 Ω. The 6 Ω branch carries 9 × 3 / (6 + 3) = 3 A and the 3 Ω branch carries 9 × 6 / 9 = 6 A. The common voltage is 3 × 6 = 18 V. The branch currents always add up to the total, which makes a handy check.

Shunt resistor

A shunt is a resistor placed in parallel with a branch to limit the current through it. The classic use is extending the range of an ammeter. To read 1 A with a movement that has a 1 mA full scale current and 50 Ω internal resistance, the shunt must be 0.001 × 50 / (1 − 0.001) = 0.05005 Ω. The second tab does this calculation.

Limits

The tool handles parallel branches between one pair of nodes. For mixed networks reduce the branches first or use the DC circuit solver. In AC circuits with inductors or capacitors the split depends on impedance, which this tool does not cover.