Question

the diameter of nichrome wire is reduced to half by stretching it the new resistance is​

Answer 1

Answer:

4 times

Explanation:

Initial resistance of the wire R=

A

ρL

Using L=

A

V

and A=

4

πd

2

⟹R=

π

2

d

4

16ρV

⟹

R

R

′

=

(d

′

)

4

d

4

(∵V,ρ are constants)

Given : d

′

=

2

d

∴ New resistance R

′

=2

4

R=16R

Answer 2

The new resistance is 8 times greater than previous resistance.

Explanation:

Nichrome Wire is an alloy mixture comprised of nickel and chromium – displays heat and corrosion-resistant characteristics, making it extremely versatile and useful in a range of applications.

• The alloy, which has highly resistive properties even at low electrical current, also has high mechanical strength and high creep strength.

• Resistance is a measure of the opposition to current flow in an electrical circuit.

• It depends on length of the material and area of cross section of the material.

• Resistance is directly proportional to the length of wire and inversely proportion to the area of cross section.

• R ∝ $\frac{1}{A}$  ⇒  R ∝ $\frac{1}{\pi r^{2} }$

• R ∝ $L$, here R is the resistance of material, r is the radius of the wire which is decreased by half and L is the length of wire which is doubled.

• $R (new)=resistivity X\frac{2L}{\pi (\frac{r}{2}) ^{2} } =resistivityX \frac{8L}{\pi r^{2} }$