Question

Two wire segments are shown; both are made of the same material and are part of a larger circuit and have an electric field $E$ across its length. However, one has a larger cross-sectional surface area, due to the radius being 3x that of the skinnier wire.
Which is true?
I. The large wire has a greater charge density.
II. The larger wire has a greater current.
III. The larger wire has low resistance.

• A. I only
• B. II only
• C. III only
• D. I and II

Answer 1

The correct option is C III only

Charge density is property of material and not of dimension and hence both will has same current density.

L=length of wire

$R=\rho \frac{L}{A}=\rho \frac{L}{\pi r^2}$

$⟹R\propto \frac{1}{r^2}$

Hence larger wire has smaller resistance.

And in the same circuit, current is same in all wires.

Hence. only option correct is $III$

Answer-(C)