Question

What happens to the resistance of carbon with rise in the temperature?
${\text{A}}{\text{.}}$ Increases
${\text{B}}{\text{.}}$ Decreases
${\text{C}}{\text{.}}$ Remains the same
${\text{D}}{\text{.}}$ First increases then decreases

Answer 1

Hint: Here, we will proceed by mentioning the two major factors on which the resistance of any material depends. Then, we will write down the effect of increase in temperature on the resistance of any semiconductor (like carbon).

Complete step-by-step answer:

There are two things impacting the resistance. The number of mobile charging carriers (typically electrons or holes) and their mobility (principally limited due to atom scattering). By increasing the temperature both the electrons and the atoms will get more energy. For both a regular metallic conductor and a semiconductor this holds true. The major difference between the two materials is the semiconductor band gap. Electrons with insufficient energy in the semiconductor can't contribute to the conductivity. By increasing the electron's energy increases the number of electrons or holes (charge carriers) that can contribute to the conductivity which will result in dramatically lowering the resistance. For metals this effect is not present.

Since the latter effect is usually much bigger than the first, while at higher temperatures there is an increase in scattering, the resistance of semiconductors decreases with increasing temperature.

All electrons are closely bound to their cores at absolute zero temperature, and the material cannot conduct current. Electrons should have some force to jump into the conduction band over the so-called band gap and be able to engage. Hence the concentration of charge carriers will increase with increasing temperature and the material's electrical resistance will decrease.

The higher temperature increases the vibration of the material's electrons (and atoms) which loosens the binding force of the electrons to the nuclei allowing them to emit and move freer with less potential.

For a material a negative coefficient means that its resistance decreases with an increase in temperature. Half-conductor materials (carbon, silicon, germanium) usually have resistance to negative temperature coefficients.

Therefore, with the rise in the temperature, the resistance of carbon (which is a semiconductor) will definitely decrease and its conductivity will definitely increase.
Hence, option B is correct.

Note: The electrical resistance of a component of a circuit is defined as the ratio of the voltage applied to the electrical current flowing through it. It would be anticipated that a wire's electrical resistance would be greater for a longer wire, less for a wire of a wider cross sectional area and would be assumed to rely on the material from which the wire is produced.