Voltage Drop in DC Circuits

Formula:

V_drop = I × R_wire
R_wire = ρ × (2L) / A

Where: - ρ = copper resistivity = 1.68 × 10⁻⁸ Ω·m - L = one-way wire length (m) - A = cross-sectional area (m²) - 2L accounts for both positive and negative conductors

Simplified (using AWG table values):

V_drop = I × (Ω_per_foot × 2L_feet)

Target: V_drop < 3% of supply voltage (< 0.36V on 12V system)

Worked example:

100A amplifier, 15-foot run, 4 AWG wire (0.025 Ω per 100 ft):

R = 0.025 × (2 × 15) / 100 = 0.0075 Ω
V_drop = 100 × 0.0075 = 0.75V (6.25%) — too high

Try 2 AWG (0.016 Ω per 100 ft):

R = 0.016 × 30 / 100 = 0.0048 Ω
V_drop = 100 × 0.0048 = 0.48V (4%) — marginal

Try 0 AWG (0.010 Ω per 100 ft):

R = 0.010 × 30 / 100 = 0.003 Ω
V_drop = 100 × 0.003 = 0.30V (2.5%) — acceptable ✓