Calculate branch currents in 2, 3, or 4 parallel resistor networks
| Branch | R (Ω) | I (A) | % of Total |
|---|
The current divider rule determines how total current splits among parallel branches. Current divides inversely to resistance: smaller resistance gets more current. This page covers the current divider formula, current divider equation, and current division with 3 resistors or more by using equivalent resistance and Ohm law.
Current division is a consequence of Kirchhoff Current Law and Ohm Law applied to parallel circuits. The total current entering a parallel network splits among branches inversely proportional to each branch resistance. The smallest resistor carries the largest current. This principle is essential for designing current-sense circuits and understanding load sharing.
For three parallel resistors, first calculate Req = 1/(1/R1 + 1/R2 + 1/R3). Then find the shared voltage V = Itotal x Req. Each branch current is In = V/Rn, or equivalently In = Itotal x Req/Rn. The same method works for any number of parallel branches.
I₁ = It × R₂/(R₁+R₂), I₂ = It × R₁/(R₁+R₂). Current through R₁ uses R₂ in numerator. Cross multiplication pattern.
Find Req = 1/(1/R₁+1/R₂+...). V = It×Req. I_n = V/R_n = It × Req/R_n. Current ∝ 1/R.
KCL requires ΣI_n = It. Always verify: I₁+I₂+... = It. If not, check calculations. This catches errors.
Using conductance G = 1/R: I_n = It × G_n/(G₁+G₂+...). Current shares proportionally to conductance (not resistance).
| Feature | Current Divider | Voltage Divider |
|---|---|---|
| Circuit type | Parallel branches | Series resistors |
| What divides | Current | Voltage |
| Main relationship | Branch current is proportional to conductance 1/R | Voltage drop is proportional to resistance R |
| Useful check | Sum of branch currents equals total current | Sum of voltage drops equals source voltage |
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