A

Step 1: Let's analyze each statement in Column-I and match it with the appropriate option from Column-II.

(i) Electrical conductivity of a conductor depends upon:
Electrical conductivity (σ) is defined as the ability of a material to conduct electric current and is affected by its physical dimensions, such as length and area of cross-section. Thus, the correct match is option [A].

(ii) Conductance of a conductor depends upon:
Conductance (G) is directly related to conductivity and inversely related to resistivity, which is influenced by temperature. Therefore, this corresponds to option [B], temperature.

(iii) For a given conductor and at given temperature, current density depends on:
Current density (J) is defined as the amount of current per unit area of cross-section of the conductor. It is influenced by the nature of the conductor, that is, its resistivity. Hence, this matches with option [C].

(iv) For a given potential difference applied across a conductor, current in it will depend on:
The current flowing through a conductor is influenced by the electric field strength (E) created by the potential difference (V) across its length. According to Ohm's law, current is proportional to the electric field strength. Therefore, this matches with option [D].

Hence, the final matching can be summarized as follows:
(i) - [A], (ii) - [B], (iii) - [C], (iv) - [D].

Final Answer: Since the question specifically asked to match electrical conductivity, conductance, current density, and current with their corresponding factors, the primary focus on (i) leads to the answer choice being A.