Question

A battery of $e m f E$ is connected across a conductor as shown. As one observes from $A$ to $B$,

Column I		Column II
i	current	p	increases
ii	drift velocity of electron	q	decreases
iii	electric field	r	remains same
iv	potential drop per unit length	s	cannot be determined

Now, match the given columns and select the correct option from the codes given below

• A. (i) - (p), (ii)- (q), (iii) - (r), (iv)- (s)
• B. (i) - (r), (ii) - (q), (iii) - (q), (iv) - (q)
• C. (i) - (q), (ii) - (p), (iii) - (s), (iv) - (r)
• D. (i) - (s), (ii) - (q), (iii) - (q), (iv) - (p)

Answer 1

Answer: (B)

Current through any cross-section should remain same as all the cross-sections are in series.
$I=n e A v_{d}$, as area increases drift velocity decreases. $E$ is directly proportional to $v_{d}$, so $E$ also decreases. If $E$ decreases, then potential difference across a segment of fixed length also decreases. This can also be done like this:

$d R=\frac{\rho d x}{A} ; A$ increases with $x$.
Potential across $d x: d V=I d R=\frac{I \rho d x}{A}$
$E=\frac{d V}{d x}=\frac{I \rho}{A} \propto \frac{1}{A}$
So $E$ and $\frac{d V}{d x}$ both decrease as $A$ increases.