Answered

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1. The electrical resistance of a wire varies
inversely as the square of its radius.
If the resistance is 0.8 ohm when the
radius is 0.4 cm, find the resistance
when the radius is 0.7 cm.
​

Sagot :

Answer:

resistance R ≈ 0.26 ohms

Step-by-step explanation:

let the resistance be R and the radius r

given R varies inversely as r² , then the equation relating them is

R = [tex]\frac{k}{r^2}[/tex] ← k is the constant of variation

To find k, substitute R= 0.8 and r = 0.4 into the equation

0.8 = [tex]\frac{k}{0.4^2}[/tex] = [tex]\frac{k}{0.16}[/tex] ( multiply both sides by 0.16 )

0.128 = k

R = [tex]\frac{0.128}{r^2}[/tex] ← equation of variation

When r = 0.7 cm , then

R = [tex]\frac{0.128}{0.7^2}[/tex] = [tex]\frac{0.128}{0.49}[/tex] ≈ 0.26 ohms ( to the nearest hundredth )

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