Q.33 Physics ⭐ 360° Option Elimination Active

NEET 2025 Physics Question 33 Solution

Topic: Current Electricity · Official NTA Booklet Code 45

Question

A wire of resistance R is cut into 8 equal pieces. From these pieces two equivalent resistances are made by adding four of these together in parallel. Then these two sets are added in series. The net effective resistance of the combination is:

✓

Verified Against NTA Final Answer Key

Option (3) : \frac{R}{16}

📚 Current Electricity Easy

📋 Given Parameters & Problem Setup

Initial Resistance of Wire R

Number of Equal Pieces 8 pieces

Grouping Scheme Two sets of 4 pieces in parallel, then the two sets connected in series

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The 30-Second Exam Hall Shortcut: ⚡ Piece Resistance & Symmetry Shortcut

⏱️ Save ~30 seconds

Each piece r = R/8. 4 in parallel: r_p = r/4 = R/32. Two identical sets in series: R_net = 2 × (R/32) = R/16!

1 Resistance of uniform wire is proportional to length: Each of the 8 pieces has resistance r = R / 8.

2 Four identical resistors of resistance r connected in parallel have equivalent resistance: R_p = r / 4 = (R / 8) / 4 = R / 32.

3 The second set of four in parallel also has equivalent resistance: R_p = R / 32.

4 These two sets are connected in series: R_net = R_p + R_p = 2 × (R / 32) = R / 16.

5 Match Option (3) in under 15 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Ohm’s Law & Resistor Networks (NCERT Physics · Current Electricity).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Calculate Resistance of Each Individual Piece

When a uniform wire of total resistance R is cut into 8 equal lengths, the cross-sectional area and resistivity remain unchanged. Therefore, each piece has resistance:

r = \frac{R}{8}

• Linear dependence: R ∝ L.

Step 2

Calculate Equivalent Resistance of Each Parallel Set

Four pieces of resistance r are connected in parallel. For n identical resistors in parallel, the equivalent resistance is r / n:

R_p = \frac{r}{4} = \frac{R / 8}{4} = \frac{R}{32}

• Both sets are identical, so each set has resistance R / 32.

Step 3

Calculate Net Resistance of the Series Combination

Connecting the two parallel sets in series gives a net resistance equal to the sum of the two resistances:

R_{net} = R_{p1} + R_{p2} = \frac{R}{32} + \frac{R}{32} = \frac{2R}{32} = \frac{R}{16}

• Matches Option (3) exactly.

⭐

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 A

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Corresponds to all 8 pieces connected in parallel (r / 8 = (R/8)/8 = R/64).

⚠️

Student Fallacy (Why candidates pick this trap): Assuming all 8 pieces were connected in parallel.

2 B

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Represents just one single set of 4 pieces in parallel, omitting the second set in series.

⚠️

Student Fallacy (Why candidates pick this trap): Stopping calculation after finding the resistance of one group.

3 C

✓ 100% Correct

Verdict & Scientific Reason:

100% correct. R_net = 2 × [(R/8)/4] = R / 16.

💡

Why this is airtight: None; systematic series-parallel reduction.

4 D

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Corresponds to the resistance of a single cut piece.

⚠️

Student Fallacy (Why candidates pick this trap): Ignoring parallel combination entirely.

⚠️

NTA Trap Alert: Forgetting the Second Group or Connecting All in Parallel

Option 1 (R/64) is chosen by students who connect all 8 pieces in parallel. Option 2 (R/32) is chosen by students who calculate one group and forget they are in series.

🛡️ How to avoid the -1 mark: Read circuit topology carefully: 2 groups of 4 in parallel, then the 2 groups in series!

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Core NEET Syllabus Standard

NEET Physics Core Syllabus · Current Electricity Standard Benchmark

Core Scientific Principle Tested:

"Parallel: 1/R_p = Σ (1/R_i); Series: R_s = Σ R_i."

Syllabus Focus: Combination of Resistors: Series and Parallel

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Cut by 8 ⟹ r = R/8. 4 in parallel ⟹ R/32. 2 in series ⟹ 2 × R/32 = R/16!

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NEET 2025 Physics Question 33 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Piece Resistance & Symmetry Shortcut

Step-by-Step Rigorous Workflow & Mathematical Proof

Calculate Resistance of Each Individual Piece

Calculate Equivalent Resistance of Each Parallel Set

Calculate Net Resistance of the Series Combination

360° Option Elimination Engine Key Feature

NTA Trap Alert: Forgetting the Second Group or Connecting All in Parallel

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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