Question

(1) A wire of 3 ohm resistance and 10 cm length is stretched to 30 cm length. Assuming that it has a uniform cross section, what will be its new resistance?
(2) A wire of 9 ohm resistance having 30 cm length is tripled on itself. What is its new resistance?
(3) What length of copper wire of resistivity 1.7x10-8ohm metre and radius 1mm is required so that its resistance is 1 ohm?

Answer 1

If resistance is R, resistivity is d, length of wire is L and A is cross section area of wire, then we can say:

R = dL/A

 When A is constant and R is directly proportional to L,

so R1/R2 = L1/L2

 R2 = (R1*L2)/L1

(1) R1 = 3 Ohm L1 = 10cm L2 = 30cm

R2 = (30*3)/10cm

R2 = 9 Ohm

  (2) Similarly,

R1 = 9 Ohm L1 = 30cm L2 = 90cm

R2 = (R1*L2)/L1

R2 = (90*3)/30cm

R2 = 27Ohm

  (3) R =1 Ohm d = 1.7× 10^-8 radius=1mm

L = RA/d

   = 1 × π( 1× 10^-3)²/(1.7× 10^-8)

  = π × 10^-6/1.7 × 10^-8

  = 100π/1.7 m = 314/17 m
   
= 18.47 m