A fuse is a thin wire made up of an alloy of lead (75 %) & tin (25 %). Both its resistance and melting point are low. It is connected in series to the circuit in to protect the circuit from sudden strong currents by breaking the circuit. When the rate at which heat produced by the current becomes equals to the rate at which heat lost by radiation, the temperature of the wire further stops increasing. This stage is called steady state, then rate of heat supplied = Rate of heat lost i.e.
(a) For constant ρ, T & Ts we can write I2 ∝ r 3, L0
(b) As TS = 0 for vacuum & other terms are constants thus T 4 ∝ r – 3 or T ∝ r – 3 / 4