Two conductors A and B of the same material ...

CBSE Class 12 Physics 2025 All Sets Solved Paper

Question : 2 of 16

Marks: +1, -0

Two conductors A and B of the same material have their lengths in the ratio 1 :2 and radii in the ratio 2 :3. If they are connected in parallel across a battery, the ratio

\frac{V_A}{V_B}

of the drift velocities of electrons in them will be

2
$\frac{1}{2}$
$\frac{3}{2}$
$\frac{8}{9}$

Solution:

The formula for drift velocity is:

V_d = \frac{I}{nAq}

Where A is the cross-sectional area. Since conductors are made of the same material, n and q are constant.

Given:

• Lengths

: l_A: l_B =1 :2

• Radii

: r_A :r_B = 2 :3

R = \frac{\rho l}{A}

⇒

I = \frac{VA}{\rho l}

⇒

\frac{VA}{\rho l} = neAv_d

⇒

V_d = \frac{V}{ne\rho l}

Here voltage v and n, e, ρ are all same for both conductor so,

V_d \propto \frac{1}{l} \Rightarrow \frac{V_A}{V_B} = \frac{2}{1}

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