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# Grounding

I constantly see people ask the questions "Can I ground my amplifier to a seat brace?" Or a random stud/bolt they come across. Even the cargo tie point bolts in the rear of an SUV.

Here's why.

Resistance of any uniform conductor is inversely proportional to cross sectional area and directly proportional to resistivity and length.
In simple words, if we increase the cross sectional area of a conductor by a factor of 2 (double the size in other words) we decrease the resistance (and voltage drop) in half. If we double the length, we will double the resistance and double the voltage drop.

A 0 (1/0) AWG copper wire has an effective diameter of about 0.3 inches. Area of a circle is pi x radius squared. This wire would have a cross sectional area of about pi*.15*.15 = .071 square inches.

Let’s assume a steel body shell is about 16 gauge, or about .06 inches thick. A one foot wide area would have 12* .06 = .72 sq. in. of cross sectional area. The physical cross section is about ten times larger than the copper wire’s cross sectional area.

The resistivity of steel is about 15 ohm per 10-6 cm.  The resistivity of copper is 1.7 ohms per 10-6 cm. We can reasonably assume steel has about 15/1.7 = 8.8 times the resistance of copper for the same length and same cross sectional area. While the body shell has higher resistance material, the body also has much greater cross sectional area.

This means a one foot wide length of steel body shell, if that shell is only .06 inches thick, has about 10% less resistance than an equal path length of copper wire. It’s easy to see why a ground path through the vehicle body, which likely is several feet wide and much thicker in many areas, is a small fraction of the resistance of a copper wire.

A four foot wide area of floor pan, just .06 inches in thickness, would have a cross section of about 2.88 square inches. The equivalent copper conductor would have to be 2.88/8.8 = .327 square inches, or a diameter  = 2*  sq rt of A/pi, or .645 inches diameter!
Equaling the resistance of a thin 4-foot wide steel floor pan with a copper cable requires a cable larger than 4/0 , and we have not even counted the help from frame rails, rocker panels, or roof paths!