Question

Please solve....

10. A copper wire has a diameter 0.5 mm and resistivity 1.6 x 10^-8 ohm

(a) What will be the length of this wire to make the resistance 12 ohm ?


(b) How much will be the resistance of another copper wire of same length but half the
diameter?
[Ans.(a) 147.3 m (b) 482)​

Answer 1

Answer:

Given, diameter, d=0.5 mm

resistivity, ρ=1.6×10

−8

Ωm

Resistance, R=10 Ω

Let the length of wire be l.

A=πd

2

/4

R=ρl/A

=

πd

2

/4

ρl

⟹l=

4ρ

Rπd

2

l=

4×1.6×10

−8

10×3.14×(0.5×10

−3

)

2

l=122 m

R∝1/d

2

If the diameter is doubled, resistance will be one-fourth.

Hence, new resistance =2.5Ω