Final answer:
The correct formula for the rate of heat generated in the wire is B. i²(Lρ/πr²), where 'i' is the current, 'ρ' is the resistivity, 'L' is the length, and 'r' is the radius of the wire.
Step-by-step explanation:
The question is about calculating the rate at which heat is generated by a current flowing through a wire with given physical properties.
The rate of heat generated by the wire is a result of the electrical resistance, which can be expressed using the resistivity (ρ), length (L), and cross-sectional area (A = πr² where 'r' is the radius of the wire).
The formula for electrical power, which is the rate of heat generation, is P = I²R, where I is the current and R is the resistance of the wire. The resistance R of the wire, using resistivity, is given by R = ρL/A.
Substituting for R and A, you get P = I²(ρL/(πr²)). Thus, the correct formula for the rate of heat generated is B. i²(Lρ/πr²).