Question

The following quantities are measured for a cylindrical wire connected in a circuit: potential difference across the wire, current in the wire, length of the wire, and cross-sectional area of the wire. Which of the following correctly indicates whether or not each quantity is needed to determine the resistivity of the wire? Current Length Area

(a) Potential Difference Yes Yes No No Potential Difference Current Length Area

(b) Yes Yes Yes Yes Potential Difference Current Length Area

(c) No No Yes Yes Potential Difference Current Length Area

(d) No No Yes No

Answer 1

To calculate resistivity, we need potential difference, current, length, and cross-sectional area, making option (b) the correct answer.

Step-by-step explanation:

To determine the resistivity of the wire, we need to consider the resistance formula for a cylindrical conductor, which is R = ρ(L/A), where R is the resistance, ρ is the resistivity, L is the length of the conductor, and A is the cross-sectional area. From Ohm's law, we know that V = IR, where V is the potential difference, and I is the current through the wire. Solving for resistivity, we get ρ = (RA)/L = (V/I)(A/L). Therefore, we need the potential difference, current, length, and cross-sectional area of the wire to determine its resistivity.

The correct answer is thus (b): Yes to needing potential difference, current, length, and area to calculate the wire's resistivity.

Answer 2

To determine the resistivity of a wire, the potential difference, current, length, and cross-sectional area of the wire are required. The correct answer to the student's question is option (b).

Step-by-step explanation:

To determine the resistivity of a wire, certain physical quantities of the wire are needed. Resistivity (ρ) is an intrinsic property of a material and depends on the material itself, not on the shape or size of the wire. According to Ohm's law, resistance (R) can be calculated using the formula R = V/I, where V is the potential difference and I is the current. The resistance of a cylindrical wire is directly proportional to its length (L) and inversely proportional to its cross-sectional area (A), given by the formula R = ρL/A. Therefore, to determine the resistivity of a wire, we need to know the potential difference (V), current (I), length of the wire (L), and cross-sectional area (A). The correct answer to the student's question is option (b).