Question

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 `v_A/v_B` of the drift velocities of electrons in them will be ______.

Options

• 2

• `1/2`

• `3/2`

• `8/9`

Answer 1

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 `v_A/v_B` of the drift velocities of electrons in them will be 2.

Explanation:

Since the conductors are connected in parallel, the voltage across them is the same:

v_A = v_B

The electric field is given by:

E = `V/L`

The ratio of the electric fields is:

`E_A/E_B = (v_A/L_A)/(v_B/L_B)`

= `v_A/L_A * L_B/v_B`

Given, `L_A/L_B = 1/2`,

Then, `L_B/L_A` = 2

∴ `E_A/E_B` = 2

The drift velocity is given by v_d = μE.

Since the conductors are made of the same material, the mobility μ is the same for both.

The ratio of the drift velocities is:

`(v_(d_A))/(v_(d_B))` = 2