Q.18 Physics ⭐ 360° Option Elimination Active

NEET 2021 Physics Question 18 Solution

Topic: Current Electricity · Official NTA Booklet Code M1

Question

The effective resistance of a parallel connection that consists of four wires of equal length, equal area of cross-section and same material is 0.25 Ω. What will be the effective resistance if they are connected in series?

✓

Verified Against NTA Final Answer Key

Option (4) : 4 Ω

📚 Current Electricity Easy

📋 Given Parameters & Problem Setup

Number of Identical Wires (n) 4

Effective Parallel Resistance (R_p) 0.25 Ω

⚡

The 30-Second Exam Hall Shortcut: ⚡ The n² Ratio Shortcut: R_s = n² R_p

⏱️ Save ~20 seconds

For $n$ identical resistors, $R_p = R/n$ and $R_s = n R \implies R_s / R_p = n^2$ . Here $n = 4$ , so $R_s = 4^2 \times R_p = 16 \times 0.25 = 4\ \Omega$ ! Instant 5-second calculation matching Option (4)!

1 Recall universal relation for

n

identical resistors:

R_s = n^2 R_p

2 Here

n = 4

and

R_p = 0.25\ \Omega = 1/4\ \Omega

3 Substitute:

R_s = 4^2 \times \frac{1}{4} = 16 \times \frac{1}{4} = 4\ \Omega

4 Match Option (4).

🛡️

Why You Can 100% Trust This Shortcut: Canonical Ohm's law rules for series and parallel networks.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Determining Resistance of an Individual Wire

Since the four wires have identical length $l$ , area $A$ , and resistivity $\rho$ , each wire has the same resistance $R = \rho l / A$ . When connected in parallel, their equivalent resistance $R_p$ is:

\frac{1}{R_p} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R} + \frac{1}{R} = \frac{4}{R} \implies R_p = \frac{R}{4}

Step 2

Calculating the Individual Resistance R

Given $R_p = 0.25\ \Omega$ :

R = 4 \times R_p = 4 \times 0.25\ \Omega = 1.0\ \Omega

Step 3

Calculating Equivalent Resistance in Series (R_s)

When the four identical wires of resistance $R = 1.0\ \Omega$ are connected in series:

R_s = R + R + R + R = 4R = 4 \times 1.0\ \Omega = 4.0\ \Omega

⭐

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

✗ Incorrect

Verdict & Scientific Reason:

This is the parallel resistance ( $R_p$ ), not the series resistance.

⚠️

Student Fallacy (Why candidates pick this trap): Assuming series and parallel configurations yield identical resistance.

2 2

✗ Incorrect

Verdict & Scientific Reason:

Result of doubling instead of applying $n^2 = 16$ multiplier.

⚠️

Student Fallacy (Why candidates pick this trap): Incorrect proportionality factor.

3 3

✗ Incorrect

Verdict & Scientific Reason:

This is the resistance of a single wire ( $R = 1\ \Omega$ ), not the four wires in series.

⚠️

Student Fallacy (Why candidates pick this trap): Finding individual resistance and forgetting to multiply by

n = 4

for series connection.

4 4

✓ 100% Correct

Verdict & Scientific Reason:

Exact series equivalent resistance: $R_s = n^2 R_p = 16 \times 0.25 = 4\ \Omega$ .

💡

Why this is airtight: None; flawless resistor network computation.

⚠️

NTA Trap Alert: Individual Resistor vs. Series Network Trap

Students frequently compute $R = 4 \times 0.25 = 1\ \Omega$ and immediately select Option (3) $1\ \Omega$ , forgetting that the question asks for all four connected in series ( $R_s = 4 \times 1 = 4\ \Omega$ ).

🛡️ How to avoid the -1 mark: Use the master ratio

R_s = n^2 R_p

directly to avoid stopping at single-resistor intermediate steps.

📖

Core NEET Syllabus Standard

NCERT Physics · Current Electricity Standard Benchmark

Core Scientific Principle Tested:

"For $n$ identical resistors, $R_s = n R$ and $R_p = R/n$ , giving the universal ratio $R_s / R_p = n^2$ ."

Syllabus Focus: Combination of Resistors - Series and Parallel

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Physics Question 18 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ The n² Ratio Shortcut: R_s = n² R_p

Step-by-Step Rigorous Workflow & Mathematical Proof

Determining Resistance of an Individual Wire

Calculating the Individual Resistance R

Calculating Equivalent Resistance in Series (R_s)

360° Option Elimination Engine Key Feature

NTA Trap Alert: Individual Resistor vs. Series Network 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

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