Studying the dependence of the current strength on the voltage across the resistor with its constant resistance

Studying the dependence of the current strength on the voltage across the resistor with its constant resistance, the student received the results presented in the table. What is the specific resistance of the metal from which the resistor is made if the wire is 10m long and its cross-sectional area is 2mm2?

L = 10 m.

S = 2 mm2.

U1 = 2 V.

U2 = 4 V.

U3 = 6 V.

I1 = 4 A.

I2 = 8 A.

I3 = 2 A.

ρ -?

R = U / I – Ohm’s law for the circuit section.

R = ρ * L / S – resistance of a homogeneous conductor.

U / I = ρ * L / S.

Let us express the specific resistance of the substance ρ from which the conductor is made: ρ = U * S / I * L.

ρ1 = U1 * S / I1 * L.

ρ1 = 2 V * 2 mm2 / 4 A * 10 m = 0.1 Ohm * mm2 / m.

ρ2 = U2 * S / I2 * L.

ρ2 = 4 V * 2 mm2 / 8 A * 10 m = 0.1 Ohm * mm2 / m.

ρ3 = U3 * S / I3 * L.

ρ3 = 6 V * 2 mm2 / 2 A * 10 m = 0.6 Ohm * mm2 / m.

Answer: the specific resistance of the metal from which the resistor is made is ρ = 0.1 Ohm * mm2 / m.