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I_total
│
├────┬────┐
┌┴┐ ┌┴┐ │
│ │ │ │ │
│R1 │R2 │
└┬┘ └┬┘ │
│ │ │
├────┴────┘
│
GND
I1↓ I2↓
(through R1) (through R2)I₁ = Itotal × R₂ / (R₁ + R₂)
I₂ = Itotal × R₁ / (R₁ + R₂)
A current divider is a circuit configuration where an input current splits among two or more parallel branches, with each branch carrying a fraction of the total current inversely proportional to its resistance. For a two-resistor current divider, the current through R₁ is I₁ = Itotal × R₂ / (R₁ + R₂). Notice the "opposite resistor" appears in the numerator — this reflects the fundamental principle that lower resistance paths carry more current. The current divider rule is the dual of the voltage divider rule: while voltage dividers split voltage proportionally to resistance, current dividers split current inversely proportional to resistance. This principle is used extensively in analog circuit design, current sensing, biasing networks, and load distribution systems.
Confirm that the resistors are connected in parallel (same two nodes). All parallel branches share the same voltage across them. Identify the total input current flowing into the parallel combination.
Find the total parallel resistance: Req = 1 / (1/R₁ + 1/R₂ + 1/R₃ + ...). For two resistors, use the shortcut Req = (R₁ × R₂) / (R₁ + R₂). This value determines the voltage across all branches.
For any branch k: Ik = Itotal × Req / Rk. For the two-resistor case, I₁ = Itotal × R₂ / (R₁ + R₂). Note that the "other" resistor's value appears in the numerator, not the branch resistor.
Check your answer by confirming that all branch currents sum to the total input current: Itotal = I₁ + I₂ + I₃ + ... If they do not add up, recheck your calculations. This verification catches arithmetic errors.
Shunt resistors used in current measurement create a current divider. A small, precise resistor diverts a known fraction of the current for measurement, allowing high currents to be monitored without inserting large resistances into the main circuit path.
When driving multiple parallel LEDs from a single current source, the current divider principle determines how current distributes among the branches. Matched resistors ensure equal brightness, while intentionally unequal resistors create dimming effects.
In analog amplifier design, current divider networks establish precise bias currents for transistors. Current mirrors, differential pairs, and active loads all rely on controlled current splitting to set operating points and achieve predictable gain.
| R₁ (Ω) | R₂ (Ω) | I₁ (A) | I₂ (A) | Req (Ω) | Ratio I₁:I₂ |
|---|---|---|---|---|---|
| 10 | 10 | 5.00 | 5.00 | 5.00 | 1:1 |
| 10 | 20 | 6.67 | 3.33 | 6.67 | 2:1 |
| 10 | 30 | 7.50 | 2.50 | 7.50 | 3:1 |
| 10 | 100 | 9.09 | 0.91 | 9.09 | 10:1 |
| 100 | 100 | 5.00 | 5.00 | 50.0 | 1:1 |
| 100 | 1000 | 9.09 | 0.91 | 90.9 | 10:1 |
| 1 | 1000 | 9.99 | 0.01 | 0.999 | 1000:1 |
A voltage divider uses series resistors where voltage is proportional to resistance (higher resistance gets more voltage). A current divider uses parallel resistors where current is inversely proportional to resistance (lower resistance gets more current). They are mathematical duals: the voltage divider formula uses the branch resistor in the numerator, while the current divider uses the opposite branch resistor.
Yes, the current divider rule applies to AC circuits by replacing resistance (R) with impedance (Z). For parallel impedances, Ik = Itotal × Zeq / Zk, where all quantities are complex numbers with magnitude and phase. This is essential for analyzing AC networks with reactive components like capacitors and inductors.
A current mirror is an active-circuit implementation of a current divider using matched transistors. It copies (mirrors) a reference current to one or more output branches with high accuracy. Current mirrors provide much higher output impedance than resistive dividers and are fundamental building blocks in analog integrated circuits for biasing and signal processing.
For N parallel resistors, first calculate the equivalent parallel resistance Req = 1 / (1/R₁ + 1/R₂ + ... + 1/RN). Then the current through any branch k is Ik = Itotal × Req / Rk. This general formula works for any number of parallel branches and always satisfies Kirchhoff's current law.
Real-world factors include resistor tolerance (typically 1–5%), temperature coefficients that change resistance with heat, contact resistance at connections, and wire resistance in the branches. For precision current division, use low-tolerance resistors (0.1% or better), and consider using a Kelvin (4-wire) connection to eliminate contact resistance effects.
Calculate output voltage for series resistor voltage divider networks used in biasing and sensing.
Find the equivalent resistance of resistors connected in parallel for circuit simplification.
Calculate current flow using Ohm's law from voltage and resistance in any electrical circuit.