Question

Consider the following statements:
(a) The specific resistance does not depend on the dimensions of a conductor.
(b) The combined resistance of any number of resistors connected in series is equal to the sum of the individual resistors.
(c) A good conductor of electricity offers more resistance.
(d) The resistance of a wire decreases with the increase in its temperature.
Which of the above statements are correct?
(A) (a) and (b)
(B) (b) and (c)
(C) (a), (b) and (c)
(D) (a), (b), (c) and (d)

Answer 1

Hint : To answer this question, we have to look for the basic definitions of each of the terms given in the statements. We have to use the relation between the conductance and the resistance of a conductor. We also have to use the equation of the temperature dependence of the resistance of a wire.

Formula used: The formula used to solve this question is given by
 $ R = {R_o}\left( {1 + \alpha \Delta T} \right) $ , here $ R $ is the final resistance, $ {R_o} $ is the initial resistance, $ \alpha $ is the temperature coefficient of resistance, and $ \Delta T $ is the change in temperature.

Complete step by step answer
We know that the specific resistance, also known as the electrical resistivity, is the property of a conductor which measures its ability to conduct or resist the electric current. It is the property of the material of a conductor, and therefore is independent of the dimensions of the conductor.
Therefore the statement (a) is correct.
Now, we know that the equivalent resistance of the combination of the resistors connected in series is obtained by adding each resistance of the individual resistances. So the combined resistance of any number of resistors connected in series is equal to the sum of the individual resistors.
Therefore the statement (b) is also correct.
We know that the conductance of a conductor is equal to the inverse of its resistance. So the greater the resistance of a conductor, the lower is its conductance. So a good conductor, which has higher conductance, will have a lower resistance, and therefore will offer less resistance.
Therefore the statement (c) is incorrect.
Finally, we know that the relation between the resistance and the temperature of a wire is given by
 $ R = {R_o}\left( {1 + \alpha \Delta T} \right) $
As the temperature coefficient of resistivity is a positive constant, so the resistance of a wire should increase with the increase in its temperature.
Therefore, the statement (d) is also incorrect.
So we see that the correct statements are (a) and (b).
Hence, the correct answer is option A.

Note
The temperature dependence of the resistance can also be investigated without using the exact equation used in the solution above. We know that the thermal energy of the atoms of a material increases with the temperature. So the vibrations of the atoms increase with the temperature, leading to increased number of collisions of the electrons with the atoms. These collisions are a restriction to the flow of electrons, and hence the resistance increases with temperature.