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If the Length of a Wire is Doubled by Taking More of Wire, What Happens to Its Resistance?

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Question

If the length of a wire is doubled by taking more of wire, what happens to its resistance?

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Solution

We know that the resistance of the wire, R = ρl / A where the resistivity of the wire is ρ.
The length of the wire = l
The area of cross-section of the wire, A = πr2
So when the length of the wire is doubled (l' = 2l) by taking more of the same wire, (it will keep the resistivity and the area of cross-section the same), the length is doubled.
New resistance = R'
R' = ρl' / A
R' = 2ρl / A
R' = 2R
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Chapter 4: Electricity - Exercise 4 [Page 213]

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Lakhmir Singh Physics Part 1 [English] Class 10
Chapter 4 Electricity
Exercise 4 | Q 2. | Page 213

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