Question

A one meter rod of 20cm diameter is drawn until its resistant is 100 times the initial resistance. What is its length afterwards?

Answer 1

Answer:

Explanation:

Diameter ÷2=radius

20÷2=20

100÷10

10

Answer 2

Given: length of rod = 1 meter

           diameter of rod = 20cm

            Final resistance = 100 times of initial resistance

To find: Final length

Solution:

• Resistance of any wire is directly proportional to the length of wire and inversely proportional to the area of cross-section of the wire and is given by the formula - R = ρL/A ( Where ρ is the resistivity of wire, L is the length of wire, and A is the area of cross-section of the wire.)
• Resistivity is the physical property of the wire and is a measure of the resisting power of a specified material that causes hindrance to the flow of an electric current.

According to the question, initial resistance R₁ = ρ (1)/πr²

radius = 10cm

Final diameter = 100/20 = 5cm

R₁ = ρ(1)/π(10)²

Final resistance R₂ = ρL₂/A

100R₁ = R₂ ( according to question)

ρ(20)/π(10)² = 100ρL₂/(2.5)²

L = 25 ×5 meters

L₂= 75 meters

Therefore, the final length of the rod is 75 meters.