Question

A certain metal wire has a cross-sectional area of 1.0 cm2 and a resistivity of 1.7 × 10-8 Ω ∙ m. How long would it have to be to have a resistance of 1.0 Ω?

Answer 1

To find the length of a metal wire with a given resistance, resistivity, and cross-sectional area, you apply the resistance formula R = ρ × (L/A). After substituting in the values and solving for L, it is found that the wire would need to be approximately 5882.35 meters long to have a resistance of 1.0 Ω.

Step-by-step explanation:

Calculating the Length of a Metal Wire for a Given Resistance

The student's question involves calculating the length of a wire which has a specific resistance, given the resistivity and the cross-sectional area of the wire. To solve this, we can use the formula for resistance in terms of resistivity:

R = ρ × (L/A)

Where:

R is the resistance (1.0 Ω)

ρ (rho) is the resistivity (1.7 × 10-8 Ω · m)

L is the length of the wire (which we need to find)

A is the cross-sectional area (1.0 cm2 = 1.0 × 10-4 m2)

By rearranging the formula to solve for L, we get:

L = R × (A/ρ)

Substituting the given values:

L = 1.0 Ω × (1.0 × 10-4 m2 / 1.7 × 10-8 Ω · m)

L = (1.0 × 10-4) / (1.7 × 10-8)

L ≈ 5882.35 meters

Therefore, the wire would need to be approximately 5882.35 meters long to achieve a resistance of 1.0 Ω.

Answer 2

L=5882.35 m

Step-by-step explanation:

Given that

Area ,A= 1 cm²

Resistivity ,ρ = 1.7 x 10⁻⁸ Ω ∙ m

Resistance ,R= 1 Ω

Lets take length of the wire = L

`R=\rho * (L)/(A)`

Resistivity =ρ

Resistance =R

Area =A

Resistance =R

`L=(R* A)/(\rho )`

Now by putting the values in the above equation get

`L=(1* 1* 10^(-4))/(1.7* 10^(-8) )\ m`

L=5882.35 m

Therefore the length of the wire will be 5882.35 m.