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

⚡

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 ↗

Ready to attempt under real exam pressure?

Test your speed and accuracy in the authentic 200-minute timed NTA simulator.

Launch NEET 2021 CBT Test →

← Previous (Q.11) All Physics Questions Grid Next (Q.13) →

🔗 Related Questions — Current Electricity

All 21 Current Electricity PYQs →

NEET 2026 Q36

Current Variation with Temperature for Series and Parallel Dual-Coefficient Resistors

View Solution →

NEET 2025 Q6

Spotted a mistake in this solution? Report an error (support@mycompetitiveexams.com)

⚖️ Legal & Fair Dealing Notice: Sourced from publicly released NEET 2021 question papers and NEET answer keys for private study, research, and non-commercial educational practice under Fair Dealing (Section 52(1)(a) of the Indian Copyright Act, 1957). Not affiliated with or endorsed by NTA or NMC.

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?

🔗 Related Questions — Current Electricity

Current Variation with Temperature for Series and Parallel Dual-Coefficient Resistors

Wheatstone Bridge Reduction & Battery Branch Current

Series and Parallel Combination of Resistor Pieces Cut from Single Wire

Current Through Cross-Connecting Wire CD in Resistor Network

Solve 4 NEET Questions a Day — One per Subject