Question

Two fuse wires have ratings of $10A$ and $13A$.Which wire has higher resistance?

Answer 1

Concept used:

1. Fuses protect household equipment against short circuits, overload, high current damage, etc. If we don't utilize fuses, electrical problems can develop in the wiring, which might cause the wire and electric equipment to catch fire and perhaps start a house fire.
2. The heating effect of the current is the basis for how fuses operate. It is constructed of a noncombustible substance with a thin strip or strand of metallic wire and is between the ends of the terminals. The electrical circuit and the fuse are always linked in series.
3. When an excessive amount of current or heat is produced as a result of heavy current flows in the circuit, the fuse melts down due to the low melting point of the element and it opens the circuit. Current flow may be stopped by an excessive flow that causes the wire to break down. The fuse can be replaced or changed with the new one with suitable ratings. . They also serve as a circuit breaker, breaking the circuit when a sudden fault develops in it.

Explanation:

1. Resistance in a conductor is directly proportional to the length of the conductor and inversely proportional to the area of the cross-section of the conductor
2. Mathematically, it can be represented as, $R=\frac{\rho l}{A}$, where, $\rho$ is the resistivity, $l$ is the length of the conductor, and, $A$ is the area of the cross-section of the conductor.
3. The resistance of a given length of flat fuse wire is inversely proportional to its thickness.
4. Therefore, increasing the thickness of a given fuse wire lowers the fuse resistance and increases the amount of current the fuse can carry without generating enough heat to burn the fuse open.
5. Thus, $13\mathrm{A}$fuse wire is thicker than $10\mathrm{A}$ fuse wire because its resistance should be smaller than$10\mathrm{A}$ fuse wire.

Therefore, $10\mathrm{A}$ wire has a higher resistance.