Calculate Branch Currents in Parallel Resistor Networks
Total Current It (A)
Number of Branches
R1 (Ω)
R2 (Ω)
Result
Branch
R (Ω)
I (A)
% of Total
Equivalent Req
Voltage V
Step-by-Step Derivation
Current Divider Formula
I_n = I_total × R_parallel / R_n
For 2 resistors: I₁ = It × R₂/(R₁+R₂)
I₂ = It × R₁/(R₁+R₂) (cross rule)
V = I_total × (1/(1/R₁+1/R₂+...))
The current divider rule determines how total current splits among parallel branches. Current divides inversely to resistance: smaller resistance gets more current. This follows from Ohm law since parallel branches share the same voltage. The two-resistor cross-rule is the most common form used in circuit analysis.
⚠Current divider is the dual of voltage divider. Voltage divider: series resistors, output proportional to R. Current divider: parallel resistors, current inversely proportional to R. Cross-rule only for 2 resistors.
Understanding Current Division
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.
Two Resistor Rule
I₁ = It × R₂/(R₁+R₂), I₂ = It × R₁/(R₁+R₂). Current through R₁ uses R₂ in numerator. Cross multiplication pattern.
General Rule
Find Req = 1/(1/R₁+1/R₂+...). V = It×Req. I_n = V/R_n = It × Req/R_n. Current ∝ 1/R.
Check Summation
KCL requires ΣI_n = It. Always verify: I₁+I₂+... = It. If not, check calculations. This catches errors.
Conductance Form
Using conductance G = 1/R: I_n = It × G_n/(G₁+G₂+...). Current shares proportionally to conductance (not resistance).
Teaching Example: It=1A, R₁=100Ω, R₂=220Ω, R₃=330Ω in parallel.
Req = 1/(1/100+1/220+1/330) = 1/(0.01+0.00455+0.00303) = 1/0.01758 = 56.9Ω.
V = 1 × 56.9 = 56.9V. I₁=56.9/100=0.569A, I₂=56.9/220=0.259A, I₃=56.9/330=0.172A.
Sum = 1.000A ✓. Smallest R (100Ω) gets most current (0.569A).
I_n = It × Req/R_n. Current divides inversely to resistance. Smaller R = more current. Verify with KCL: sum of branches = It.
How to find current in 2 parallel resistors?▼
I₁ = It × R₂/(R₁+R₂), I₂ = It × R₁/(R₁+R₂). Cross rule: I through R₁ uses R₂ in numerator.
Current divider vs voltage divider?▼
Voltage divider: series R, Vout ∝ R. Current divider: parallel R, I_branch ∝ 1/R. They are dual circuits. Cross rule applies to both.
What if one resistor is zero?▼
A short circuit (R=0) takes ALL current. The parallel combination becomes 0Ω. All current bypasses the other resistors. This is a short circuit condition.
Free online calculators and tools covering mathematics, unit conversion, text processing, and daily life. Accurate, fast, mobile-friendly, and completely free to use.