Question

resistavity of iron wire 20×10⁶ohm cm and its cross -sectional area is 0.02cm² . if its resistance is 10ohm, then find out the length of wire .​

Answer 1

Given:

• Resistivity of Iron wire, ρ = 20 × 10⁶ Ω cm
• Area of cross section of wire, A = 0.02 cm²
• Resistance of Wire, R = 10 Ω

To find:

• Length of the wire, L =?

Knowledge required:

• Relation between Resistivity (ρ), Resistance (R), Length of conductor (L) and area of cross section of conductor (A)

        R = ρ L / A

[ Where R is in ohms, ρ is in ohm metre, L is in metres and A is in metre square; these are their SI units ]

Solution:

▶ Converting Resistiivty and area of cross-section into their SI units

→ ρ = 20 × 10⁶ Ω cm

→ ρ = 20 × 10⁶ × 10⁻²  Ω m

→ ρ = 20 × 10⁴  Ω m

and,

→ A = 0.02 cm²

→ A = 0.02 × 10⁻⁴  m²

▶ Calculating Length of Wire

→ R = ρ L / A

→ L = R A / ρ

→ L = ( 10 ) ( 0.02 × 10⁻⁴ ) / ( 20 × 10⁴ )

→ L = ( 0.2 × 10⁻⁴ ) / ( 20 × 10⁴ )

→ L = 0.01 × 10⁻⁸ m

Therefore,

• Length of Wire would be 0.01 × 10⁻⁸ metres.

Answer 2

Answer:

Explanation:

Solution:

Resistivity of Iron wire, ρ = 20 × 10⁶ Ω cm

Area of cross section of wire, A = 0.02 cm²

Resistance of Wire, R = 10 Ω

Length of the wire, L =?

As we know that:

Relation between Resistivity (ρ), Resistance (R), Length of conductor (L) and area of cross section of conductor (A)

       R = ρ L / A

[ Where R is in ohms, ρ is in ohm metre, L is in metres and A is in metre square; these are their SI units ]

or, ρ = 20 × 10⁶ Ω cm

or,ρ = 20 × 10⁶ × 10⁻²  Ω m

∴ρ = 20 × 10⁴  Ω m

Now,

A = 0.02 cm²

 A = 0.02 × 10⁻⁴  m²

Next,

R = ρ L / A

or,L = R A / ρ

or,L = ( 10 ) ( 0.02 × 10⁻⁴ ) / ( 20 × 10⁴ )

or, L = ( 0.2 × 10⁻⁴ ) / ( 20 × 10⁴ )

∴ L = 0.01 × 10⁻⁸ m

So,

Length of Wire would be 0.01 × 10⁻⁸ metres.