Question

A metallic wire is subjected to increase its length 150% of older length and diameter reduced by 60% of older diameter. 120 ohm, then calculte resistance. If old resistance is 120
ohm, then calculate the new resistance.​

Answer 1

New resistance is 1125 Ω if A metallic wire of resistance 120 Ω  is subjected to increase its length 150% of older length and diameter reduced by 60% of older diameter

Given:

• A metallic wire is subjected to increase its length 150% of older length and diameter reduced by 60% of older diameter.
• old resistance is 120 ohm

To Find:

• New Resistance

Solution:

• R = ρL/A
• R = Resistance
• ρ = Resistivity
• L = Length
• A = Area
• A = πd²/4  where d is the diameter

Step 1:

Assume Old Length and diameter  are L and d respectively and resistivity is ρ , Hence

120 = ρL/(πd²/4)

=> 30 =  ρL/(πd²)

Step 2:

Calculate new length  L'

L' = 150 % of L

L' = (150/100)L

L' = 3L/2

Step 3:

Calculate new diameter

d' = d -  60 % of d

d' =  d - (60/100)d

d' = 2d/5

Step 4:

Find new resistance

R' =  ρL'/A'

R' =  ρL'/(πd'²/4)

R' =  4ρL'/(πd'²)

Step 5:

Substitute L' = 3L/2 and d' = 2d/5

R' =  4ρ(3L/2)/(π(2d/5)²)

R' =  75ρL/2πd²

R' =  (75/2)ρL/(πd²)

Substitute ρL/(πd²) = 30

R' =  (75/2)30

R' = 75 x 15

R' = 1125

Hence, New resistance is 1125 Ω