Question

a wire of resistivity 10 ohm is stretched to double its length.what is the new resistivity?

Answer 1

Concept:

The Greek letter rho, ρ is frequently used to represent resistivity, which is numerically equivalent to the resistance R of a wire-like specimen, multiplied by its cross-sectional area A, and divided by its length l; ρ = RA/l. The ohm is the measurement of resistivity.

Given:

The resistivity of wire = 10 ohm

Find:

We need to determine the new resistivity when the length of the wire is doubled.

Solution:

We know the equation-

R = ρL/A where R is the resistance, ρ is the resistivity, L is the length and A is the area of cross-section.

Arranging in terms of resistivity it becomes -

ρ = RA/L = 10 ohm

We know, ρ = 10 ohm therefore, ρ = RA/L = 10 ohm for wire of length L

If the length of the new wire = 2L

Therefore, the equation of resistance becomes-

R = ρ2L/A

Therefore,

Resistivity, ρ = RA/2L

ρ = 1/2 RA/L

We have, RA/L = 10 ohm

Therefore, ρ = 10/2 = 5 ohm

Thus, the new resistivity becomes 5 ohm

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Answer 2

Answer:

New resistivity is $5$ohm m.

Explanation:

It is given that:

The resistivity of wire = $10$ ohm m

We need to determine the new resistivity when the length of the wire is doubled.

ρ is  used to represent resistivity, which is numerically equivalent to the resistance R of a wire-like specimen, multiplied by its cross-sectional area A, and divided by its length l.

Mathematically,

ρ$= RA/l$

ρ = $RA/L = 10$

If the length of the new wire = $2l$

Resistivity becomes ρ = $RA/2L$

ρ $= 10/2 = 5$

New resistivity is $5$ohm m.

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