How the Current Divider Rule Works
When two resistors are connected in parallel, they share the same voltage across their terminals because both are connected between the same pair of nodes. The total current flowing into the parallel combination splits between the two branches in inverse proportion to their resistance. This means the branch with the lower resistance carries more current, since current through each resistor equals the shared voltage divided by that resistor's own resistance (Ohm's law).
The Current Divider Formula
For two resistors R1 and R2 in parallel with total current I flowing into the combination:
| Quantity | Formula |
|---|
| Current through R1 | I1 = I × R2 / (R1 + R2) |
| Current through R2 | I2 = I × R1 / (R1 + R2) |
| Equivalent resistance | Req = (R1 × R2) / (R1 + R2) |
| Voltage across the pair | V = I × Req |
Notice that each branch current formula uses the resistance of the OTHER branch in the numerator. This is the opposite of the voltage divider rule, where each resistor's own value appears in the numerator of its own voltage. The two branch currents always add up exactly to the original total current I, which follows directly from Kirchhoff's current law.
Worked Example
With a total current of 1 A flowing into two resistors in parallel, R1 = 100 ohms and R2 = 200 ohms:
- Equivalent resistance: Req = (100 × 200) / (100 + 200) = 20000 / 300 = 66.67 ohms
- Current through R1: I1 = 1 × 200 / 300 = 0.667 A (667 mA)
- Current through R2: I2 = 1 × 100 / 300 = 0.333 A (333 mA)
- Voltage across the pair: V = 1 × 66.67 = 66.67 V
Note that R1 is the smaller resistor and carries the larger share of current (0.667 A versus 0.333 A), confirming that current favours the path of least resistance.
Why Use a Current Divider
Current dividers are used in electronics to split a known current between two parallel paths, such as sharing load current across parallel resistors for power dissipation reasons, setting bias currents in transistor circuits, or building simple analogue current-sensing shunts. Unlike a voltage divider, a current divider is normally driven by a current source or by a circuit that behaves like one at the node in question, rather than a voltage source directly across both resistors.
Extending to More Than Two Resistors
For more than two resistors in parallel, the general current divider formula for any branch k is Ik = I × Rtotal_parallel / Rk, where Rtotal_parallel is the equivalent resistance of the whole parallel network (including or excluding branch k depending on the derivation used) or, more commonly, is expressed using conductances: Ik = I × Gk / (G1 + G2 + ... + Gn), where Gk = 1 / Rk. This calculator handles the common two-resistor case directly.
Related Calculators
Sources: Current divider rule derived from Ohm's law (V = IR) and Kirchhoff's current law, standard results found in any introductory electrical engineering or circuit analysis textbook.
This calculator assumes ideal resistors with no internal source resistance and a total current supplied to the parallel combination. Real circuits with a voltage source and additional series resistance may need the equivalent resistance combined with the rest of the circuit before applying the current divider rule.
