Q.48 Physics ⭐ 360° Option Elimination Active

NEET 2023 Physics Question 48 Solution

Topic: Current Electricity · Official NTA Booklet Code G5

Question

10 resistors, each of resistance R are connected in series to a battery of emf E and negligible internal resistance. Then those are connected in parallel to the same battery, the current is increased n times. The value of n is:

✓

Verified Against NTA Final Answer Key

Option (3) : 100

📚 Current Electricity Easy

📋 Given Parameters & Problem Setup

Number of identical resistors (N) 10

Resistance of each resistor R

Battery EMF and internal resistance E, r = 0

Current ratio I_parallel / I_series = n

⚡

The 30-Second Exam Hall Shortcut: ⚡ Series to Parallel Current Scaling: n = N²

⏱️ Save ~35 seconds

R_series = N R and R_parallel = R / N ⟹ I_parallel / I_series = (N R) / (R / N) = N² = 10² = 100 in 5 seconds!

1 Equivalent resistance in series for N identical resistors: R_s = N R = 10 R.

2 Current in series: I_s = E / (10 R).

3 Equivalent resistance in parallel for N identical resistors: R_p = R / N = R / 10.

4 Current in parallel: I_p = E / (R / 10) = 10 E / R.

5 Current magnification factor: n = I_p / I_s = (10 E / R) / (E / 10 R) = 10 × 10 = 100.

6 Lock Option (3) 100 immediately!

🛡️

Why You Can 100% Trust This Shortcut: Current Electricity · Ohm’s Law & Resistor Grouping (Current ratio for N identical resistors between parallel and series across an ideal voltage source is strictly n = N²).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Series Combination Analysis

When 10 identical resistors of resistance R are connected in series, the equivalent resistance R_s is the direct sum of all individual resistances:

R_s = R + R + \dots + R = 10 R

Step 2

Current Drawn in Series Configuration

Connected across an ideal battery of EMF E with negligible internal resistance, the circuit current I_s is given by Ohm’s Law:

I_s = \frac{E}{R_s} = \frac{E}{10 R}

Step 3

Parallel Combination Analysis

When the same 10 resistors are connected in parallel, the reciprocal sum yields equivalent resistance R_p:

\frac{1}{R_p} = \sum_{i=1}^{10} \frac{1}{R} = \frac{10}{R} \implies R_p = \frac{R}{10}

Step 4

Current Drawn in Parallel Configuration

Connected across the same battery of EMF E, the circuit current I_p is:

I_p = \frac{E}{R_p} = \frac{E}{\frac{R}{10}} = \frac{10 E}{R}

Step 5

Evaluation of Current Multiplication Factor n

The problem states that I_p = n I_s. Taking the ratio:

n = \frac{I_p}{I_s} = \frac{\frac{10 E}{R}}{\frac{E}{10 R}} = 10 \times 10 = 100

⭐

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:

Overestimates by a factor of 10 (N³ instead of N²).

⚠️

Student Fallacy (Why candidates pick this trap): Candidate computed 10³ = 1000.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Current in each individual parallel branch increases by 1, or candidate thought n = N.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate assumed current increases by N = 10 times instead of N² = 100.

3 (3)

✓ 100% Correct

Verdict & Scientific Reason:

Accurate multiplication factor: n = N² = 10² = 100.

💡

Why this is airtight: None. Candidate correctly recognized the N² ratio.

4 (4)

✗ Incorrect

Verdict & Scientific Reason:

Absurd claim that current remains unchanged.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate confused power with current or made a wild guess.

⚠️

NTA Trap Alert: Thinking Current Increases by N = 10 Times Instead of N² = 100 Times

In parallel, each branch draws E/R (which is 10× the series current E/10R). Since there are 10 parallel branches, the TOTAL battery current is 10 × (10 E/10R) = 100 × I_series! Confusing branch current with total current leads to Option (2) 10.

🛡️ How to avoid the -1 mark: Universal Rule: For N identical resistors, R_s / R_p = N² ⟹ I_p / I_s = N².

📖

Core NEET Syllabus Standard

National Eligibility cum Entrance Test (NEET UG) · Current Electricity Standard Benchmark

Core Scientific Principle Tested:

"Series resistance is N R; parallel resistance is R/N. Current ratio across constant voltage is N²."

Syllabus Focus: Resistors in Series and Parallel

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Physics Question 48 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Series to Parallel Current Scaling: n = N²

Step-by-Step Rigorous Workflow & Mathematical Proof

Series Combination Analysis

Current Drawn in Series Configuration

Parallel Combination Analysis

Current Drawn in Parallel Configuration

Evaluation of Current Multiplication Factor n

360° Option Elimination Engine Key Feature

NTA Trap Alert: Thinking Current Increases by N = 10 Times Instead of N² = 100 Times

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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