Question

In general, when the temperature of a conductor increases, its resistance
A. increases
B. decreases
C. remains the same with rise
D. first increases then decreases.

Answer 1

Hint: We can see from the derived formula of resistance from Ohm’s law, that the resistance only depends on the current passed and the voltage of the circuit. But this won’t work as there is no mention of temperature in this formula. We have to think in a general way that if we heat up a wire what will happen and how will it affect the resistance of the circuit.

Formula used:
V = I R
$R=\rho \dfrac{l}{A}$

Complete answer:
We know that resistance is the property of a circuit / conductor which opposes the flow of current through the circuit / conductor.
According to ohm’s law,
V = I R,
Or
R = V / I.
We see that resistance is dependent on voltage and current of the circuit.
We also know that resistance is,
$R=\rho \dfrac{l}{A}$,
But here we see that resistance depends upon the length of the conductor and its cross-sectional area.
Now, in general if we increase the temperature of a conductor the resistance also increases because, as the temperature rises the thermal velocity of the free electron also increases. And due to this increase in velocity the number of collisions between the free electrons also increases. And as the collisions increases the free flow of current is also decreased and as a result resistance increases.

Now, considering option A, which says that resistance increases,
This option is the correct option according to the explanation given above.

Considering option B: decreases
This option is incorrect as it says that when the temperature increases the resistance decreases according to the above explanation it is incorrect.

Considering option C: Remains the same with rise
This option is also incorrect, as whenever the temperature increases to whatever extent the resistance also increases.

Considering option D: First increases then decreases
According to the explanation given above this option is also incorrect as with rise in temperature resistance will always increase.

So, the correct answer is “Option A”.

Note:
In the formula V = I R, ‘V’ is the voltage or potential difference of the circuit. ‘I’ is the current in the circuit and R is the resistance. And in the formula $R=\rho \dfrac{l}{A}$, $\rho $ is the resistivity of the wire or conductor it is a fixed quantity, $l$ is the length of the wire or conductor, and $A$ is the cross sectional area.