Question

A copper wire has a diameter of 0.5 mm and resistivity of 1.6 × 10 -8  m. (a) What

will be the length of this wire to make its resistance 10  ?​

Answer 1

The word "apparent" means "as observed at a particular point X". Different observers will observe different frequencies depending on their relative velocity to the source. This doesn't change the frequency of the sound that is generated; just the frequency of the sound that arrives at the ear of the observer.

Answer 2

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Given:

Copper wire,

• diameter = d = 0.5 mm
• Resistivity = ρ = 1.6 ohm m
• Resistance = R = 10 Ω

To find:

Length of wire = ?

Solution:

$\\ \\ R \: = ρ \dfrac{l}{ A} \\ \\ where \: R \: = resistance \\ \\ ρ = resistivity \\ \\ l = length \: of \: material \\ \\ A = area \: of \: material$

Radius = Diameter/2

Radius = 0.5/2 = 0.25 mm

1m = 1000 mm

0.25 mm = 0.25/1000 = 0.25 × 10^-3 m

A = πr² = 3.14× (0.25 × 10^-3)² = 0.19625 m²

$\\ \\ R \: = ρ \dfrac{l}{ A} \\ \\l = \dfrac{ \:R \times A}{ ρ } \\ \\ l = \dfrac{10 \times 0.19625}{1.6}$

$\\ \\ l = \dfrac{1.9625}{1.6} \\ \\ l = 1.226 \: m$

Required answer:

Thus, length of wire to make resistance 10 Ω is 1.226 m

Knowledge booster:

• SI unit of resistance is ohm and it is represented by Ω and inverse of resistance is conductance
• SI unit of resistivity is ohm meter and inverse of resistivity is conductivity
• Try to solve more such questions to remember formula