a) Your lab partner is confused about current stuff. Help him out. A lab extensi

Question

a) Your lab partner is confused about current stuff. Help him out. A lab extension question reads “If current in a conducting wire is doubled, by how much does the a) charge carrier density, b) the current density, c) the electron drift speed, d) power dissipated, e) resistivity, f) electron current, and g) the average time between collisions change?” b) Two unequal resistors – one twice the resistance of the other - are connected in series and attached to a battery to form a complete circuit. How do the currents in the two resistors compare? How do you know? c) Sally Sue and Betty Lou both believe that current density must be conserved in the same way that current is, that is, the same everywhere in any series circuit. What is an example that you can give that is contrary to their thinking and shows it isn’t necessarily so? d) Since Ohm’s Law has been given the title of “Law”, we know that it must be true in all situations. Agree or not? Explain briefly.

Explanation / Answer

(a) charge carrier density denoted the number of charge carriers per volume. If current in a conducting wire is doubled, this means number of charge carrriers are also doubled, so charge carrier density doubles.

(b) current density is electric current per unit area. As electric current doubles, current density doubles.

(c) drift speed = (current density) / (charge carrier density * charge on an electron)

as current doubles, current density density and so does the charge carrier density, this means drift speed remain the same.

(d) P=I2R, as current doubles, power becomes 4 times of what it originally was.

(e) resistivity is inversely proportional to the current. So when current doubles, resistivity becomes half of its original value.

(f) electron current is same as that of electric current, so it doubles.

(g) From Drude model, average time between collisionsc is directly proportional to current density. As current density doubles when current doubles, average time between collisions also doubles.

(b) since the resistors are connected in series, the same current will flow through the circuit.

(c) the electric current is flow of electrons which in turn are the charges. Charges and hence current must be conserved, but on the contrary current density if current per unit area. The cross sectional area of the wire may not be same althrough the circuit. hence it is not necessary that in a series circuit, the current density will be conserved at every point in the circuit.

(d) Agree. The law must hold in all the situations, as it has been validated for variety of circuits under different temperature and other variable conditions.

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