Question

In a safety fuse the temperature to which the wire gets heated is inversely proportional to the
a)radius of the wire b)cube of the radius of the wire c)square of the radius of the wire d)fourth power of the radius of the wire

Answer 1

Dear Student,

An electrical fuse works on the principle of heat produced while current flows through it.
As heat produced in wire is given as
$$\begin{gathered} H=I^{2}RT \\ \Rightarrow H=I^2\frac{\rho l}{A}T \\ \Rightarrow H=I^2\frac{\rho l}{\pi r^2}T \end{gathered}$$
where r is the radius of wire.
Thus the temperature to which wire gets heated is inversely proportional to square of radius of the wire.

Regards