Question

Calculate the resistance of 1 km long copper wire of radius 1 mm.
$resistivity \: of \: copper \: = \: {10}^{ - 8}$
​

Answer 1

Resistance = 3.184713 ohm ( Ω )

Formula

Resistance of wire will be = Resistivity x Length of wire / Area of wire

• Resistance = 10^-8 x 1 km / π r²
• Resistance = 10^-8 x 1000000 millimetres / 3.14 x 1 milimitre²
• Resistance = 10^-8 x 10^6 / 3.14 milimetre
• Resistance = 0.01 / 3.14
• Resistance = 0.01 / 3.14
• Resistance = 0.003184 mm^-1

Converting to ohm-metre ,

• Resistance = 0.003184 / 0.001 metre
• Resistance = 3.184713 ohm ( Ω )

Answer 2

Answer:

3.18 Ω

Explanation:

As we know,

R = ∅ L/A

where, R is the Resistance.

∅ is the Resistivity

L is the Length of the wire

A is the Area of cross section.

According to question:

L = 1 Km = 1000m

$radius \: (r) \: = \: 1mm \: = \: {10}^{ - 3} m$

$area \: = \: \pi {r}^{2} \\ = \: 3.14 \times {( {10}^{ - 3} )}^{2} \\ = \: 3.14 \times {10}^{ - 6} {m}^{2} \\ resistivity \: = \: {10}^{ - 8}$

So,

$resistance \: = \: {10}^{ - 8} \times 1000 \: \div \: (3.14 \times {10}^{ - 6} ) \\ = \: 10 \div 3.14 \\ = \: 3.18 \: ohm$

Thanks!