Question : If a conducting wire of length 10 cm and resistance 10 ohm is stretched by 10% more, then determine resistance of the new wire.
Doubt by Deepanshi U
Solution :
l = 10 cm
R = 10 Ω
l' = l + 10% of l
l' = l + 0.1 l
l' = 1.1 l
Also, the Volume of the wire remains same.
V = Al = A'l'
A' = Al/l'
A' = Al/1.1l
A ' = A/1.1
New Resistance, R'
R' = ρl'/A'
R' = ρ1.1l/(A/1.1)
R' = ρ(1.1×1.1)l/A
R' = 1.21(ρl/A)
R' = 1.21×R [ R = ρl/A]
R' = 1.21×10
R' = 12.1 Ω
Shortcut Method
R' = n2R
n = 1.1
R = 10 Ω
R' = n2×R
R' = (1.1)2×R
R' = 1.21×10
R' = 12.1 Ω
