A domestic lighting circuit is designed so that the load current should never exceed

PHYSICS · Multi-part · CBSE · Physics · Electricity: Magnetic and Heating Effects · Electricity: Magnetic and Heating Effects

Problem

10\,\text{A}

. The copper wires used for the circuit have a radius of

1.5\,\text{mm}

. A separate fuse is to be made from nichrome (resistivity

1.1\times10^{-6}\,\Omega\,\text{m}

). The fuse is required to melt when the current reaches

12\,\text{A}

. Experiments show that the nichrome alloy melts when the power dissipated in it reaches

25\,\text{W}\,\text{cm}^{-1}

of its length. The intended length of the fuse element is

4\,\text{cm}

. (a) Calculate the maximum resistance the fuse element may have without melting. (b) Hence determine the radius of the nichrome fuse wire that will satisfy the above condition. Express your answer in millimetres, correct to two significant figures. (c) Briefly state two reasons, based on your calculations, why it is safe to connect this fuse in series with the much thicker copper house wiring.

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