Question

The graph below shows the variation of current density (J) with electric field (E) applied to two different metallic wires A and B.

1. Which one of the wires, A or B, has higher resistivity?
2. For a certain value of electric field (E), in which wire ‘A’ or ‘B’ is drift velocity greater? Give a reason for your answer.

Answer 1

a. Applying in microscopic form (vector form), we have:

E = PJ

or P = `E/J`

⇒ P ∝ `1/J`

Wire B has a greater current density (J).

∴ P_A > P_B

or

The resistivity of wire A > The resistivity of wire B.

b. J = `E/P`

⇒ `I/A = E/P`

⇒ `(n e Av_d)/A = E/P`

∴ Drift velocity, v_d = `E/(n eP)`

⇒ v_d ∝ `1/P`

Drift velocity of wire B > Drift velocity of wire A (due to higher current density J)