Question

A circuit employing a copper wire of 2mm² cross-section is protected by a lead fuse wire of 0.2mm² cross-section. The short circuit current is 30A. How long after a short circuit does the lead fuse melt? How much does the temperature of the copper wire rise during this time? Take the specific heat of lead to be constant and equal to 0.032 and of copper 0.091; the resistivity of lead 22 x 10^-6Ω cm, of copper 1.7 x 10^-6Ωcm; the melting point of lead 327°C. The temperature of the conductors before the short circuit is 20°C. The density of copper is 8.9 g/cm³ and of lead 11.34g/cm³. Neglect the loss of heat due to thermal conductivity. 

Answer 1

where C₁ and d₁ are the specific heat and density of lead. The equations for the heating of the copper wire have the same form.