The electrical resistance of a copper wire varies directly with its length and inversely with the square of the diameter of the wire. If a wire 20 m long with a diameter of 4 mm has a resistance of 35 , find the resistance of a wire 30 mm long with a diameter of 4.5 mm. Round your answer to two decimal places.
A) 39.64
B) 40.26
C) 41.48
D) 42.35

Question

The electrical resistance of a copper wire varies directly with its length and inversely with the square of the diameter of the wire. If a wire 20 m long with a diameter of 4 mm has a resistance of 35  , find the resistance of a wire 30 mm long with a diameter of 4.5 mm. Round your answer to two decimal places.
A) 39.64 
B) 40.26 
C) 41.48 
D) 42.35

Quizplus · Accepted Answer

According to the problem, we have the equation:

R = k * (L/d^2)

where R is the resistance, L is the length, d is the diameter, and k is the constant of proportionality.

Using the values given, we can find k:

35 = k * (20/0.004^2)

k = 35 * 0.004^2 / 20 = 0.0014

Now, we can use this value of k to find the resistance of the other wire:

R = 0.0014 * (30/0.0045^2) = 41.48

Therefore, the answer is choice C.

The Electrical Resistance of a Copper Wire Varies Directly with Its