Explain the following.
$(a)$ Why is the series arrangement not used for domestic circuits?
$(b)$ How does the resistance of a wire vary with its area of cross-section?

(N/A) In a series circuit,the total voltage is divided among the components. If one component fails or is switched off,the entire circuit breaks,and no current flows. Furthermore,each device receives a lower voltage than required,and the total resistance increases,which reduces the current. Therefore,series arrangement is not used in domestic circuits.
$(b)$ The resistance $(R)$ of a wire is inversely proportional to its area of cross-section $(A)$. This is expressed as $R \propto \frac{1}{A}$. As the area of cross-section increases,the resistance decreases,and vice versa.