Question

Technician A says that resistance increases as the diameter of a conductor increases. Technician B says that resistance increases as the temperature of a conductor increases. Which technician is correct?

Answer 1

Step-by-step explanation:

Resistance is defined as the ability of a substance to resist the flow of current through the substance. Formula to calculate resistance is as follows.

R =
`(\rho l)/(A)`

As outer surface of a wire is in the shape of sphere. therefore, its area will be as follows.

A =
`4 \pi r^(2)`

or, A =
`4 \pi ((d)/(2))^(2)`

where, d = diameter of the sphere

This means that with increase in diameter of a conductor there will occur an increase in area of the wire. As area is inversely proportional to resistance so, increase in area will lead to a decrease in resistance.

On the other hand, relation between resistivity and temperature is as follows.

`\rho \propto (1)/(d) \propto A^(2) \propto T`

where,
`\rho` = resistivity

d = mean free path of electrons

A = amplitude of atomic vibrations

T = temperature

Also, resistivity is directly proportional to resistance. So, with increase in temperature there will occur an increase in resistance of the conductor.

Thus, we can conclude that only technician B is correct.