Question

At the same temperature, two wires made of pure copper have different resistances. The same voltage is applied at the ends of each wire. The wires may differ in
Check all that apply.
length.
cross-sectional area.
resistivity.
amount of electric current passing through them

Answer 1

Concepts and reason

The main concepts required to solve this problem are the ohm’s law, current, resistivity, resistance, length and cross-sectional area.

Initially, write the equations for the ohm’s law and the equation for the relation of the resistivity and the resistance. Use these two equations and explain the incorrect options which does not differ in and finally find the correct options those differ.

Fundamentals

The equation for the Ohm’s law is,

$R = \frac{V}{I}$

Here, R is the resistance, V is the voltage and I is the current through the wire.

The equation for the relation of the resistivity and the resistance is,

$R = \frac{{\rho L}}{A}$

Here, L is the length of the wire, A is the cross-sectional area of the wire, $\rho$ is the resistivity of the wire and R is the resistance of the wire.

Ohm’s law states that the current passing through conducting wire is directly proportional to the voltage and the inversely proportional to the resistance of the wire.

If the voltage increase, the current increases and if the resistance increases, the current will decrease.

The equation for the Ohm’s law is,

$R = \frac{V}{I}$ …… (1)

The resistance in the wire is directly proportional to the resistivity and length of the wire and the inversely proportional to the cross-sectional area of the wire.

The equation for the relation of the resistivity and the resistance is,

$R = \frac{{\rho L}}{A}$ …… (2)

The Ohm’s law equation is,

$R = \frac{V}{I}$

Here, for the different resistances of the two copper wires and the same voltage, then the current may differ in the wires.

The relation of the resistivity and the resistance of the wire is,

$R = \frac{{\rho L}}{A}$

Here, as the resistances are different two copper wires, the length of the wire and the cross-sectional area of the wires will be differed. Here, resistivity is constant for the both wires as the two wires are made of the copper.

Therefore, above explanation, the current, length, cross-sectional area may differ in the wires.

Ans:

The current, length and cross-sectional area may differ in wires.