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 2700ft long with a diameter of 0.26 inches is 9850 ohms, what is the resistance of 2800ft of the same type of wire with a diameter of 0.1 inches? (leave k in fraction form or round to at least 3 decimal places. round off your final answer to the nearest hundredth.)

R is proportional to the length of the wire:

R ∝ length

R is also proportional to the inverse square of the diameter:

R ∝ 1/diameter²

The resistance of a wire 2700ft long with a diameter of 0.26in is 9850Ω. Now let's change the shape of the wire, adding and subtracting material as we go along, such that the wire is now 2800ft and has a diameter of 0.1in.

Calculate the scale factor due to the changed length:

k₁ = 2800/2700 = 1.037

Scale factor due to changed diameter:

k₂ = 1/(0.1/0.26)² = 6.76

Multiply the original resistance by these factors to get the new resistance:

R = R₀k₁k₂

R₀ = 9850Ω, k₁ = 1.037, k₂ = 6.76

R = 9850(1.037)(6.76)

R = 69049.682Ω

Round to the nearest hundredth:

R = 69049.68Ω

+15-35=-20

going in opposite directions

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