what is the resistance of 2400 ft of the same type of wire with a diameter of 0.34 inches?

Question

The resistance, R, of a wire varies directly as its length and inversely as the square of its diameter. If the resistance of a wire 3500 ft long with a diameter of 0.29 inches is 18952 ohms, what is the resistance of 2400 ft of the same type of wire with a diameter of 0.34 inches? (Leave k in fraction form or round to at least 3 decimal places. Round off your final answer to the nearest hundredth.)

Answer 1

The relationship is 

 

R = cL / d²

 

where L = length, d = diameter, and c = a constant

 

Find c from the given information:

 

c = Rd² / L = (18952 ohms) (0.29 inches)² / (3500 ft) = 0.4554 ohms*inches²/ft

 

Then for L = 2400 ft and d = 0.34 inches,

 

R = cL / d² = (0.4554 ohms*inches²/ft) (2400 ft) / (0.34 inches)² = 9454.67 ohms