(a) A copper wire has diameter 0.5 mm and resistivity of 1.6 × 10-8Q
m. What will be the length of this wire to make its resistance 10 2?
How much does the resistance change if the diameter is doubled?
Answers
Ans: Area of cross-section of the wire, A =π (d/2) 2
Diameter= 0.5 mm = 0.0005 m
Resistance, R = 10 Ω
We know that,
R= rho L/A
L=RA/rho
= 10*3.14*(0.0005/2)2 ............(the whole square)
1.6*10 raised to -8
= 10*3.14*25 = 122*72
4*1.6
∴ length of the wire = 122.72m
If the diameter of the wire is doubled, new diameter=2×0.5=1mm=0.001m
Let new resistance be Rʹ
R'=rho L/A
=1.6*10 raised -8 *122.72
π(1/2*10 raise -3)2............(the whole square)
=106*10 raise -8*122.72*4
3.14*10 raise -6
=250.2* 10 raise -2= 2.5Ω
hope it helps!!!
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Here's your answer mate
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