Final answer:
The correct answer to the student's question is that statement (a) is correct because doubling the voltage across a resistor will double the current, according to Ohm's law. Statement (b) is wrong because if wire A has twice the cross-sectional area of wire B, wire B will have half the resistance of wire A, not twice.
Step-by-step explanation:
Analysis of Statements on Voltage, Current, and Resistance
The first part of the question deals with Ohm's law, which states that the current (I) through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. The formula derived from Ohm's law is I = V/R. Therefore, if the voltage across a resistor is doubled and the resistance remains the same, the current will also double. This makes statement (a) correct.
Moving on to statement (b), the resistance of a wire is given by the formula R = ρL/A, where ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area. If two copper wires have the same length and material but different cross-sectional areas, and wire A has twice the cross-sectional area of wire B, this implies that wire B will have twice the resistance of wire A. This statement is wrong because if wire A has twice the cross-section, it should have half the resistance of wire B, not twice.
Therefore, the answer to the question is (ii): a) is correct and b) is wrong.