Answer:
0.648 ohms
Step-by-step explanation:
As a wire gets longer its resistance increases,
150 ft = 16.2 ohms
1 ft = 16.2/150 ohms
6ft = 16.2(6)/150 ohms
6ft = 0.648 ohms
A wire of resistance of 16.2Ω when 150 ft. long, will have a resistance of 0.648Ω when its length is 6 ft.
Two terms are directly proportional when the increase in one increases the other term, and the decrease in one decreases the other term.
Two terms are inversely proportional when the increase in one decreases the other term and the decrease in one increases the other term.
We are informed that a 150 ft. long wire has a resistance of 16.2Ω.
We know that the length of the wire (say l) is directly proportional to its resistance (say R), that is,
R ∝ l.
To remove the sign of proportionality, we multiply the R.H.S. with a constant k.
R = kl.
We are given when l = 150 ft., R = 16.2Ω. Substituting these values,
16.2 = k*150
or, k = 16.2/150 = 0.108.
In the new case, we are asked to find the resistance R, given length l = 6 ft.
R = kl = 0.108*6 = 0.648Ω.
∴ Resistance of 6 ft. of the given wire = 0.648Ω.
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