Q.12 Physics ⭐ 360° Option Elimination Active

NEET 2021 Physics Question 12 Solution

Topic: Current Electricity · Official NTA Booklet Code M1

Question

Column - I gives certain physical terms associated with flow of current through a metallic conductor. Column - II gives some mathematical relations involving electrical quantities. Match Column - I and Column - II with appropriate relations. Column - I: (A) Drift Velocity (B) Electrical Resistivity (C) Relaxation Period (D) Current Density. Column - II: (P) m/(ne²ρ) (Q) nevd (R) (eE/m)τ (S) E/J

✓

Verified Against NTA Final Answer Key

Option (1) : (A)-(R), (B)-(S), (C)-(P), (D)-(Q)

📚 Current Electricity Easy

📋 Given Parameters & Problem Setup

Column I (A) Drift Velocity, (B) Electrical Resistivity, (C) Relaxation Period, (D) Current Density

Column II (P) m / (n e^2 ρ), (Q) n e v_d, (R) e E τ / m, (S) E / J

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The 30-Second Exam Hall Shortcut: ⚡ Microscopic Formula Matcher

⏱️ Save ~25 seconds

Match standard NCERT microscopic expressions: Drift velocity $v_d = \frac{eE}{m}\tau$ (R); Resistivity $\rho = \frac{E}{J}$ (S); Current density $J = n e v_d$ (Q); Relaxation time $\tau = \frac{m}{n e^2 \rho}$ (P)! Instant 10-second match to Option (1)!

1 Drift velocity formula:

v_d = \frac{eE}{m}\tau \implies (A)-(R)

2 Ohm's law in microscopic form:

E = \rho J \implies \rho = \frac{E}{J} \implies (B)-(S)

3 Current density formula:

J = \frac{I}{A} = n e v_d \implies (D)-(Q)

4 Relaxation time: from

\rho = \frac{m}{n e^2 \tau} \implies \tau = \frac{m}{n e^2 \rho} \implies (C)-(P)

5 Match combination: (A)-(R), (B)-(S), (C)-(P), (D)-(Q) -> Option (1).

🛡️

Why You Can 100% Trust This Shortcut: Canonical Drude-Lorentz free electron theory and microscopic Ohm's law.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Formula for Drift Velocity (A)

Under an applied electric field $\vec{E}$ , the electric force on an electron is $-e\vec{E}$ , imparting acceleration $\vec{a} = -e\vec{E}/m$ . The average velocity acquired over relaxation time $\tau$ is:

v_d = a\tau = \frac{eE}{m}\tau \implies \mathbf{(A)-(R)}

Step 2

Formula for Electrical Resistivity (B)

In vector microscopic notation, Ohm's law states $\vec{J} = \sigma \vec{E} = \frac{1}{\rho}\vec{E}$ . Rearranging gives electrical resistivity:

\rho = \frac{E}{J} \implies \mathbf{(B)-(S)}

Step 3

Formula for Current Density (D)

Electric current is $I = n e A v_d$ . Dividing by cross-sectional area $A$ gives the current density:

J = \frac{I}{A} = n e v_d \implies \mathbf{(D)-(Q)}

Step 4

Formula for Relaxation Period (C)

Microscopic resistivity in terms of electron mass $m$ , charge $e$ , number density $n$ , and relaxation time $\tau$ is $\rho = \frac{m}{n e^2 \tau}$ . Solving for $\tau$ gives:

\tau = \frac{m}{n e^2 \rho} \implies \mathbf{(C)-(P)}

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 1

✓ 100% Correct

Verdict & Scientific Reason:

Flawless 1-to-1 correspondence with the canonical NCERT microscopic current equations.

💡

Why this is airtight: None; textbook verbatim matching.

2 2

✗ Incorrect

Verdict & Scientific Reason:

Swaps relaxation period (C) and current density (D).

⚠️

Student Fallacy (Why candidates pick this trap): Mismatched (C) and (D).

3 3

✗ Incorrect

Verdict & Scientific Reason:

Mismatches resistivity (B) with formula for relaxation period.

⚠️

Student Fallacy (Why candidates pick this trap): Confusing

\rho

and

\tau

4 4

✗ Incorrect

Verdict & Scientific Reason:

Scrambles multiple associations.

⚠️

Student Fallacy (Why candidates pick this trap): Random pairing.

⚠️

NTA Trap Alert: Relaxation Time Inversion Trap

Students frequently remember $\rho = \frac{m}{n e^2 \tau}$ and get confused when Column II presents $\tau = \frac{m}{n e^2 \rho}$ , mistaking it for resistivity.

🛡️ How to avoid the -1 mark: Cross-multiply:

\tau = \frac{m}{n e^2 \rho}

. It matches Relaxation Period directly.

📖

Core NEET Syllabus Standard

NCERT Physics · Current Electricity Standard Benchmark

Core Scientific Principle Tested:

"Drift velocity is $v_d = \frac{eE}{m}\tau$ , current density is $J = n e v_d$ , and resistivity is $\rho = \frac{E}{J} = \frac{m}{n e^2 \tau}$ ."

Syllabus Focus: Drift of Electrons and the Origin of Resistivity

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Physics Question 12 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Microscopic Formula Matcher

Step-by-Step Rigorous Workflow & Mathematical Proof

Formula for Drift Velocity (A)

Formula for Electrical Resistivity (B)

Formula for Current Density (D)

Formula for Relaxation Period (C)

360° Option Elimination Engine Key Feature

NTA Trap Alert: Relaxation Time Inversion Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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