2. A wire of length l and resistance R is stretched to get
the radius of cross-section halved .What is the new
resistance of the wire after stretching?
Answers
New resistance of the wire after stretching is 16 times if radius of cross-section halved
Explanation:
Let say initial radius of cross section of wire = r & Length =l
Area of cross section A = πr²
Resistance R = ρ l/A
Now wire is stretched to get the radius of cross-section halved
Volume of wire will remain same
V = Cross section Area * Length
=> V = πr² * l
Now new radius rₙ = r/2
New length lₙ = ?
Hence πr² * l = π(r/2)² * lₙ
=> lₙ = 4l
New cross section Aₙ = π(r/2)² = πr²/4 = A/4
Aₙ = A/4
New resistance of wire Rₙ = ρ lₙ/Aₙ
= ρ 4l /(A/4)
= 16 ρ l/A
= 16 R
Rₙ = 16 R
Hence New Resistance become 16 more times
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