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Current Electricity question

2022 · 27 Jul · Shift 2 · Q50
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Current Electricity question

2022 · 27 Jul · Shift 2 · Q50

JEE MainPhysicsCurrent ElectricityMCQ+4 / −1
(A) The drift velocity of electrons decreases with the increase in the temperature of conductor. (B) The drift velocity is inversely proportional to the area of cross-section of given conductor. (C) The drift velocity does not depend on the applied potential difference to the conductor. (D) The drift velocity of electron is inversely proportional to the length of the conductor. (E) The drift velocity increases with the increase in the temperature of conductor. Choose the correct answer from the options given below :
  1. A
    (A) and (B) only
  2. B
    (A) and (D) only
  3. C
    (B) and (E) only
  4. D
    (B) and (C) only
View written solutionFree

Correct answer: B

  1. Use the formula for drift velocity

For a conductor, I=neAvdI = n e A v_dI=neAvd​ so vd=IneA.v_d = \frac{I}{n e A}.vd​=neAI​.

Also, using Ohm's law, I=VR,R=ρLAI = \frac{V}{R}, \qquad R = \rho \frac{L}{A}I=RV​,R=ρAL​ therefore I=VAρL.I = \frac{V A}{\rho L}.I=ρLVA​.

Substituting into drift velocity:

= \frac{V}{n e \rho L}.$$ So for a given material and applied potential difference, $$v_d \propto \frac{1}{L}.$$ --- 2. **Check statement (A)** Statement: *The drift velocity of electrons decreases with increase in temperature of conductor.* In a metallic conductor, with increase in temperature, relaxation time decreases and resistivity increases. For a given applied potential difference, $$v_d = \frac{e E \tau}{m}$$ or equivalently drift velocity decreases as temperature increases. So **(A) is correct**. --- 3. **Check statement (B)** Statement: *The drift velocity is inversely proportional to the area of cross-section of given conductor.* From $$v_d = \frac{I}{n e A},$$ if current $I$ is fixed, then indeed $v_d \propto \frac{1}{A}$. But for a **given conductor** connected to a potential difference, current itself depends on area: $$I = \frac{V A}{\rho L}.$$ Then $$v_d = \frac{V}{n e \rho L},$$ which is **independent of area**. Hence **(B) is false** in this context. --- 4. **Check statement (C)** Statement: *The drift velocity does not depend on applied potential difference.* From $$v_d = \frac{V}{n e \rho L},$$ we see $$v_d \propto V.$$ So **(C) is false**. --- 5. **Check statement (D)** Statement: *The drift velocity of electron is inversely proportional to the length of the conductor.* From $$v_d = \frac{V}{n e \rho L},$$ for fixed $V$ and material, $$v_d \propto \frac{1}{L}.$$ So **(D) is correct**. --- 6. **Check statement (E)** Statement: *The drift velocity increases with increase in temperature of conductor.* This is opposite to (A), and for a metallic conductor under fixed applied potential difference it is false. So **(E) is false**. --- 7. **Correct option** The correct statements are: - **(A)** correct - **(D)** correct Therefore the correct option is: $$\boxed{\text{B: (A) and (D) only}}$$
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