A nichrome wire has a resistance of 6 ohm. Find the resistance of another nichrome
wire six times longer and the area of the cross section of which is double than that of
the first.
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Answer:
Given:
Nichrome wire has resistance of 6 ohm.
To find:
Resistance of another nichrome wire having six times length and double area of cross section.
Formulas used:
R = ρ(l/a) ,
where "ρ" is resistivity, "l" is length and "a" is area of cross section.
Assumptions:
The temperature of the surroundings are considered constant. In that case , the resistivity will remain constant.
Calculation:
let initial length be l1 and initial area be a1.
So resistance R1 = ρ(l1/a1) = 6 ohm
New length l2 = (6 × l1)
New area a2 = (2 × a1)
New resistance
= R2
= ρ(l2/a2)
= ρ{(6× l1)/(2 × a1)}
=3 × [ρ(l1/a1)]
= 3 × 6
= 18 ohms.
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