Question

The resistivity of a 1.0 m long wire is 1.72 × 10-8 ωm and its cross sectional area is 2.0 × 10-6 m2. if the wire carries a current of 0.20 a, what is the voltage across the wire?

Answer 1

The voltage across the wire is 1.72 x $10^{-3}$ V

What does the Resistance of a wire depend on ?

The resistance of a wire is the opposition to the flow of current. It depends on the following;

• Temperature

• Length of the wire

• Cross sectional area

• Resistivity of the wire

Given that the resistivity of a 1.0 m long wire is 1.72 × 10-8 ωm and its cross sectional area is 2.0 × 10-6 m2. if the wire carries a current of 0.20A

The given parameters are;

• Resistivity ρ = 1.72 × 10-8 ωm

• Length L = 1.0 m

• Cross sectional area A = 2.0 × $10^{-6}$ m²

• Current I = 0.2 A

• Resistance R = ?Voltage V = ?

The formula to use to get R will be

R = ρL / A

Substitute all the necessary parameters into the formula

R = 1.72 x $10^{-8}$ x 1 / 2 x $10^{-6}$

R = 8.6 x $10^{-3}$  Ω

From Ohm's law, V = IR

Substitute all the necessary parameters into the formula

V = 0.2 x 8.6 × $10^{-3}$

V = 1.72 x $10^{-3}$ V

Therefore, the voltage across the wire is 1.72 x $10^{-3}$ V

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