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zhuklara [117]
3 years ago
12

The resistance, R, of a wire varies directly as its length and inversely as the square of its diameter. If the resistance of a w

ire 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.)
Physics
1 answer:
lbvjy [14]3 years ago
8 0

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

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3 years ago
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To balance the equation, the number of atoms of each element in the right side equation should be equal to left. By putting the numerical coefficient of 2, you will distribute that to each element. So you will end up with 2 nitrogen atoms and 2 oxygen atoms on the left side of the equation. Thus, the equation is balanced. 

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