$(a)$ $(i)$ What is meant by saying that the potential difference between two points is $1 \, V$? $(ii)$ How much energy is given to $5 \, C$ of charge passing through a $12 \, V$ battery? $(b)$ Describe an activity with a necessary electric circuit to study the factors on which the resistance of a conducting wire depends.

(A) $(i)$ It means that the work done in moving a charge of $1 \, C$ between the two points is $1 \, J$.
$(ii)$ Using the formula $W = qV$,where $q = 5 \, C$ and $V = 12 \, V$,we get $W = 5 \times 12 = 60 \, J$.
$(b)$ To study the factors affecting resistance:
$(i)$ Set up a circuit with a cell,an ammeter,a nichrome wire of length $l$,and a plug key.
$(ii)$ Close the key and note the current reading in the ammeter.
$(iii)$ Replace the wire with another nichrome wire of the same thickness but double the length $(2l)$. Note the current.
$(iv)$ Replace the wire with a thicker nichrome wire of the same length $l$. Note the current.
$(v)$ Replace the wire with a copper wire of the same length and thickness as the first nichrome wire. Note the current.
$(vi)$ Observe that the current varies in each case,demonstrating that resistance depends on length,cross-sectional area,and the material of the conductor.