The Current Divider Rule (CDR) states that the current through any branch in a parallel circuit is inversely proportional to the resistance of that branch.
For two resistors R₁ and R₂ in parallel with total current Itotal:
I₁ = Itotal × (R₂ / (R₁ + R₂))
I₂ = Itotal × (R₁ / (R₁ + R₂))
For multiple resistors, the current through Rₓ is:
Iₓ = Itotal × (Rtotal / Rₓ)
Where Rtotal = 1 / (1/R₁ + 1/R₂ + ... + 1/Rₙ)
Example: Three resistors in parallel: R₁=10Ω, R₂=20Ω, R₃=30Ω with Itotal=1A
1. Calculate total resistance: 1/Rtotal = 1/10 + 1/20 + 1/30 = 0.1 + 0.05 + 0.0333 = 0.1833
Rtotal = 1 / 0.1833 ≈ 5.4545Ω
2. Calculate branch currents:
I₁ = 1A × (5.4545/10) ≈ 0.5455A
I₂ = 1A × (5.4545/20) ≈ 0.2727A
I₃ = 1A × (5.4545/30) ≈ 0.1818A
For AC circuits, the same principle applies but using impedance (Z) instead of resistance:
Iₓ = Itotal × (Ztotal / Zₓ)
Where Ztotal = 1 / (1/Z₁ + 1/Z₂ + ... + 1/Zₙ)
Impedance is a complex quantity with both magnitude and phase: Z = R + jX
This calculator uses only the magnitude of impedance for simplification.