Voltage Drop in DC Circuits

Formula:

V_drop = I * R_wire
R_wire = rho * (2L) / A

Where:

• rho = 1.68 * 10^-8 ohm*m for copper
• L is one-way wire length
• A is conductor cross-sectional area
• 2L accounts for both positive and negative conductors

Simplified using AWG table values:

V_drop = I * (ohms_per_foot * 2 * L_feet)

Target: keep voltage drop under about 3% of supply voltage (under 0.36 V on a 12 V system).

Worked example:

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

R = 0.025 * (2 * 15) / 100 = 0.0075 ohm
V_drop = 100 * 0.0075 = 0.75 V (6.25%) - too high

Try 2 AWG (0.016 ohm per 100 ft):

R = 0.016 * 30 / 100 = 0.0048 ohm
V_drop = 100 * 0.0048 = 0.48 V (4.0%) - marginal

Try 0 AWG (0.010 ohm per 100 ft):

R = 0.010 * 30 / 100 = 0.0030 ohm
V_drop = 100 * 0.0030 = 0.30 V (2.5%) - acceptable