At a voltage of 2 V, the current flowing through a metal conductor 2 m long is 1 A. What will be the current through

| August 16, 2021 | education

At a voltage of 2 V, the current flowing through a metal conductor 2 m long is 1 A. What will be the current through the same conductor 1 m long with a voltage of 4 V on it?

U1 = 2 V.

l1 = 2 m.

I1 = 1 A.

l2 = 1 m.

U2 = 4 V.

I2 -?

According to Ohm’s law for a section of the circuit, the current in the conductor I is directly proportional to the voltage at its ends U and inversely proportional to the resistance of the conductor R: I = U / R.

I2 = U2 / R2.

I1 = U1 / R1.

The resistance R of a cylindrical homogeneous conductor is determined by the formula: R = ρ * l / S, where ρ is the resistivity of the material from which the conductor is made, l is the length of the conductor, S is the cross-sectional area of ​​the conductor.

Since the resistivity ρ and the cross-sectional area S of the conductor does not change, but only its length changes, then R1 = ρ * l1 / S, R2 = ρ * l2 / S.

I1 = U1 * S / ρ * l1.

S / ρ = I1 * l1 / U1.

I2 = U2 * S / ρ * l2 = U2 * I1 * l1 / U1 * l2.

I2 = 4 V * 1 A * 2 m / 2 V * 1 m = 4 A.

Answer: the current in the conductor will be I2 = 4 A.



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