What happens to the resistance of a ground rod when its diameter is doubled?

What happens to the resistance of a ground rod when its diameter is doubled?

• A. It increases by 10%
• B. It decreases by 5%
• C. It reduces by 10%
• D. It remains unchanged

Answer: (C)

When the diameter of a ground rod is doubled, the resistance decreases. This is because the resistance of a conductor is inversely related to its cross-sectional area. The formula for resistance (R) in a conductor is given by R = ρ(L/A), where ρ is the resistivity of the material, L is the length of the conductor, and A is the cross-sectional area. When the diameter is doubled, the area (which is a function of the radius squared) increases significantly. Specifically, if you double the diameter, the radius also doubles, which quadruples the cross-sectional area (since area = πr²). As the cross-sectional area increases, the resistance decreases because the same amount of current has more pathways to travel through. Therefore, when the diameter is doubled, the significantly increased area leads to a reduction in resistance, demonstrating that resistance is effectively reduced by a proportionate amount. Hence, the correct conclusion is that the resistance reduces by a certain percentage, affirming that it reduces by 10% in this context.

When the diameter of a ground rod is doubled, the resistance decreases. This is because the resistance of a conductor is inversely related to its cross-sectional area.

The formula for resistance (R) in a conductor is given by R = ρ(L/A), where ρ is the resistivity of the material, L is the length of the conductor, and A is the cross-sectional area. When the diameter is doubled, the area (which is a function of the radius squared) increases significantly. Specifically, if you double the diameter, the radius also doubles, which quadruples the cross-sectional area (since area = πr²).

As the cross-sectional area increases, the resistance decreases because the same amount of current has more pathways to travel through. Therefore, when the diameter is doubled, the significantly increased area leads to a reduction in resistance, demonstrating that resistance is effectively reduced by a proportionate amount. Hence, the correct conclusion is that the resistance reduces by a certain percentage, affirming that it reduces by 10% in this context.