Current Dividers

DC Circuits · 9 min read

Voltage dividers split a source voltage between series resistors. Current dividers do the dual job — they split a source current between parallel branches. The rule for which branch gets the bigger share is the opposite of what most people guess: more current goes through the smaller resistor.

The two-branch formula

For a source current $I_{src}$ splitting between two parallel resistors $R_1$ and $R_2$ , the current through $R_1$ is:

I_1 = I_{src} \cdot \frac{R_2}{R_1 + R_2}

Notice the flip — the fraction has the other branch's resistance on top. That's the entire counter-intuitive kernel: small branches pull more current, so their share of the total is larger, which means the other resistance sits in the numerator when you solve for this branch's slice.

Symmetrically, the current through $R_2$ is:

I_2 = I_{src} \cdot \frac{R_1}{R_1 + R_2}

Check: $I_1 + I_2 = I_{src}$ — KCL at the fan-out node holds, as it must.

Why the flip — conductance view

The cleanest way to see the divider is to think in conductance ( $G = 1/R$ ) instead of resistance. A parallel combination's total conductance is the simple sum $G_{total} = G_1 + G_2 + \ldots$ , and each branch's share of the source current is exactly its share of the total conductance:

I_k = I_{src} \cdot \frac{G_k}{G_{total}}

Plug in $G = 1/R$ and the resistance version falls out, with the flip baked in because you're dividing reciprocals. Whether you prefer conductance or resistance is taste; the resistance form wins on schematics, the conductance form wins on intuition.

N-branch generalisation

For $N$ parallel branches the resistance-form formula has to use the equivalent parallel resistance of the other branches rather than a single $R_j$ :

I_k = I_{src} \cdot \frac{R_{\text{others}}}{R_k + R_{\text{others}}}

That gets fiddly fast. For three or more branches, it's usually cleaner to just compute the voltage across the parallel bank — $V = I_{src} \cdot R_{total}$ — and then take $I_k = V / R_k$ for each branch. Same answer, zero book-keeping.

Current dividers are KCL in a sharper suit.

I_k = I_{src} \cdot G_k / G_{total}

. Smaller resistor, bigger current share — the opposite instinct from voltage dividers.

Common uses

Shunt ammeter. A precision low-value resistor in parallel with a meter movement diverts most of the current away from the movement, letting a microammeter read large currents.
Current steering in LED banks. A current-limited supply sits across several LED strings; each string's share is set by its ballast resistor (bigger R → less current → dimmer). Precision dimming without a variable supply.
Analog signal attenuation. Sometimes it's cleaner to divide a known current and recover voltages downstream than to divide a voltage directly — especially with low-impedance sensors.