Question

what is the resistance of a copper wire of length 200m and cross section 1mm^2 . resistivity of copper is 1.62×10^(-8) ohms meter​

Answer 1

Answer:

• Resistance of wire = 3.24 ohms

Explanation:

Given:

• Length of copper wire, L = 200 m
• Area of cross section, A = 1 mm² = 1 ×10⁻⁶  m²
• Resistivity of copper wire, ρ = 1.62 × 10⁻⁸ Ω m

To find:

• Resistance of wire, R =?

Formula required:

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

       R = ρ L / A

Calculation:

Using formula

→ R = ρ L / A

→ R = ( 1.62 × 10⁻⁸ ) ( 200 ) / ( 1 × 10⁻⁶ )

→ R = 324 × 10⁻⁸ / 10⁻⁶

→ R = 324 × 10⁻²

→ R = 3.24 Ω

Therefore,

• Resistance of wire is 3.24 ohms.

Answer 2

$\huge\bf{\underbrace{\gray{GIVEN:-}}}$

• Length of a copper wire (l) = 200 m

• Area of cross section of the wire (A) = 1 mm² .

• Resistivity of the wire ($\bf{\rho}$) = 1.62 × $\bf{10^{-8}}$ Ω.m

$\huge\bf{\underbrace{\gray{TO\:FIND:-}}}$

• The Resistance of the copper wire .

$\huge\bf{\underbrace{\gray{SOLUTION:-}}}$

We have know that,

$\green\bigstar{\gray{\overbrace{\underbrace{\purple{Resistance(R)\:=\:\rho\:\dfrac{l}{A}\:}}}}}$

Where,

• $\bf\red{\rho}$ = 1.62 × $\bf{10^{-8}}$ Ω.m

• $\bf\red{l}$ = 200 m

• $\bf\red{A}$ = 1 mm² = $\bf{1\times{10^{-6}}\:m^2}$

$\rm{:\implies\:Resistance\:(R)\:=\:1.62\times{10^{-8}}\times{\dfrac{200}{10^{-6}}}\:}$

$\rm{:\implies\:Resistance\:(R)\:=\:1.62\times{10^{-8}}\times{200}\times{10^6}\:}$

$\rm{:\implies\:Resistance\:(R)\:=\:324\times{10^{-2}}\:\Omega\:}$

$\bf\green{:\implies\:Resistance\:(R)\:=\:3.24\:\Omega\:}$

$\huge\red\therefore$ The Resistance of the copper wire is "3.24 Ω" .