$(a)$ In the circuit shown, connect a nichrome wire of length $L$ between points $X$ and $Y$ and note the ammeter reading.
$(i)$ When this experiment is repeated by inserting another nichrome wire of the same thickness but twice the length $(2L)$, what changes are observed in the ammeter reading?
$(ii)$ State the changes that are observed in the ammeter reading if we double the area of cross-section without changing the length in the above experiment. Justify your answer in both cases.
$(b)$ "Potential difference between points $A$ and $B$ in an electric field is $1\, V$." Explain the statement.

(N/A) $(i)$ The ammeter reading will decrease (become half). This is because resistance $R$ is directly proportional to length $L$ $(R \propto L)$. When length is doubled, resistance doubles, and according to Ohm's law $(I = V/R)$, the current $I$ becomes half.
$(ii)$ The ammeter reading will increase (become two times). This is because resistance $R$ is inversely proportional to the area of cross-section $A$ $(R \propto 1/A)$. When the area is doubled, resistance becomes half, and consequently, the current $I$ becomes double.
$(b)$ It means that $1\, J$ of work is being done to move a charge of $1\, C$ from point $A$ to point $B$.