Electronics
Current divider rule explained
A current divider is two or more resistors in parallel sharing one current. Every branch has the same voltage across it, so the current splits in inverse proportion to the resistances: the smaller resistor takes the bigger share. For two branches, I1 = I × R2 ÷ (R1 + R2).
The current divider rule
Notice the other resistor sits on top. That's the opposite of the voltage divider, where a resistor's own value goes on top.
Example: 12 mA flows into 1 kΩ in parallel with 3 kΩ.
The 3 kΩ takes the other 3 mA. Check with Kirchhoff's current law: 9 + 3 = 12 mA, everything that went in comes out. And the ratio of the currents is the inverse ratio of the resistors: three times the resistance, a third of the current.
Why it works
Parallel branches connect across the same two points, so they share one voltage. Find it first and the branch currents follow from Ohm's law:
Then 9 V ÷ 1 kΩ = 9 mA and 9 V ÷ 3 kΩ = 3 mA. The rule is just this shortcut written in one line.
For three or more branches, use conductance, G = 1 ÷ R, in siemens. Each branch takes its conductance's share: Ik = I × Gk ÷ (G1 + G2 + G3).
Live experiment
Switch on the branches
Three LEDs share one 9 V battery, each on its own branch with its own switch and resistor, about 10 mA apiece. Switch them on one at a time: the ones already on don't dim, and the battery's current adds up branch by branch.
“Parallel circuits” is lesson 2 of 7 in Junction City, Electronics World 2. Free with an account. Lessons unlock in order, so you’ll do the 8 before it first.
Voltage source or current source?
The rule assumes you know the total current. With a battery, you usually know the voltage instead, and that's even easier: every branch gets the full voltage, and its current is V ÷ R on its own. Add a branch and the others don't change; the battery just supplies more. (A real battery sags a little under a big load, so in practice they dim slightly.)
The total current really is shared only when something fixes it, like a current source or a big resistor feeding the group. Then a new branch does take its share from the others.
Where you'll meet it
Ammeters measure big currents with a shunt: a tiny resistor in parallel with the meter, so only a small, known share of the current passes through the meter itself. And parallel LEDs each need their own resistor: share one, and the LED with the lowest forward voltage takes nearly all the current while a blue one beside a red one never lights.
Free lesson
Now build it yourself
Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.
“Parallel circuits” is lesson 2 of 7 in Junction City, Electronics World 2. Free with an account. Lessons unlock in order, so you’ll do the 8 before it first.
Or start from the very first lesson, no account neededWork it out
- Resistors in series and parallel calculatorThe total of up to eight resistors, in series or in parallel.
- Series and parallel resistors practice problemsTotals in series and parallel, mixed networks and branch currents, all worked.
- Kirchhoff's laws practice problemsBalance currents at a junction and voltages round a loop, with the working for each.
Practice questions
Three quick questions from the lessons. Pick an answer to check it.
Show the answer
Answer: both their ends connect to the same two points. Parallel means both ends share the same two nodes, however the drawing looks. Series parts are on one path, so they always share the same current. Equal currents alone don't prove either.
- Why not “the same current flows through them”? Equal currents don't prove anything. Series parts share one current, and parallel parts only carry equal currents when their resistances match.
- Why not “they're drawn next to each other”? How the parts are drawn doesn't matter. Two resistors drawn side by side can still be in series if they don't share both ends.
Show the answer
Answer: 9 V. Side by side, the voltage stays at one battery's worth. Only a chain adds volts.
- Why not “0 V”? Both batteries push the same way across the load, so it gets their shared 9 V, not nothing.
- Why not “4.5 V”? Parallel batteries don't split the voltage between them. Each one holds the full 9 V across the load.
- Why not “18 V”? Volts only add when batteries are chained + to −. Side by side, both sit across the same two points.
Show the answer
Answer: either is closed. In parallel, the current has two paths, so either closed switch completes the loop. That's an OR gate made of switches. In series, both must close, and that's AND.
- Why not “both are closed”? Needing both closed is switches in series, an AND. In parallel, either path completes the loop on its own.
- Why not “neither is closed”? With neither closed there's no path at all, so the lamp stays dark.
“Parallel circuits” is lesson 2 of 7 in Junction City, Electronics World 2. Free with an account. Lessons unlock in order, so you’ll do the 8 before it first.
Questions people ask
What is the current divider formula?
For two resistors in parallel fed a total current I, the current through R1 is I × R2 ÷ (R1 + R2), and through R2 it's I × R1 ÷ (R1 + R2). Each branch's share has the other resistor on top, so the smaller resistor takes the bigger share.
How is a current divider different from a voltage divider?
A voltage divider is resistors in series sharing a voltage, and the bigger resistor gets the bigger share. A current divider is resistors in parallel sharing a current, and the smaller resistor gets the bigger share, because it's the easier path.
Does adding a parallel branch take current from the others?
Not on a steady voltage supply. Every branch still has the full voltage across it, so its current, V ÷ R, doesn't change, and the supply simply provides more in total. It only steals if the total current is fixed, as from a current source.
How do I split current between more than two branches?
Use conductance, G = 1 ÷ R. Each branch takes its conductance's share of the total: I_k = I × G_k ÷ (G1 + G2 + G3 + ...). Or find the voltage across the group first, V = I × R_parallel, then each branch current is V ÷ R.
Related topics
- Series vs parallel circuitsOne path or many: what stays the same, what adds up, and how to combine resistors.
- Kirchhoff's laws explained: KCL and KVLWhat flows into a junction flows out, and the drops round a loop add up to the rise.
- Voltage divider explainedTwo resistors that split a voltage: the formula, potentiometers, and why a load drags the output down.
- How to calculate equivalent resistanceShrink any series-parallel network to one resistor, one step at a time, and spot what's really in parallel.