Question

a) How does use of fuse wires protect the electric appliances?
b) Name the factors on which the resistance depends?

Answer 1

- Hint: We all know that electric appliances work on current and a current passing through a conductor generates heat. Heat generated in a wire (conductor) is directly proportional to the square of the current flowing in it.

Complete step-by-step solution -
a) Fuse wires are used to protect the electrical appliances from the sudden increase in the current, which can damage the appliances. When current flows through a wire or any conductor, heat is generated within the wire due to the current. The heat generated in the wire is directly proportional to the square of the current flowing through it. Therefore, if the current in the circuit increases, more heat will be generated in the appliances and this can cause damages to the circuits of the appliances.
Therefore, the best solution to this problem is to switch off the circuit when the current exceeds a certain value. The fuse wires do this job. Fuse wires have a lower melting point than the other components of the circuits. These fuse wires are connected in series with the other components. When the current in the circuit is too much, the heat generated by this current will melt the fuse wire and there is a break in the circuit. Thus, the current is stopped from flowing before it damages the appliances.
b) Resistance (R) of a wire depends on the resistivity ($\rho$) of the material of the wire. It is directly proportional to the resistivity of the material. It also depends on the length (l) and cross sectional area (A) of the wire. Resistance of a wire is directly proportional to its length and is inversely proportional to its cross sectional area.
i.e. $R\propto \rho$
$R\propto l$
$R\propto \dfrac{1}{A}$
And $R=\rho \dfrac{l}{A}$

Note: Resistivity of a material ($\rho$) can be considered as constant at a given temperature. If the temperature is increased, the resistivity of the good conductors decreases and vice-versa. For semiconductors, as the temperature increases, the resistivity also increases.