Q.19 Physics ⭐ 360° Option Elimination Active

NEET 2021 Physics Question 19 Solution

Topic: Current Electricity · Official NTA Booklet Code M1

Question

In a potentiometer circuit a cell of EMF 1.5 V gives balance point at 36 cm length of wire. If another cell of EMF 2.5 V replaces the first cell, then at what length of the wire, the balance point occurs?

✓

Verified Against NTA Final Answer Key

Option (1) : 60 cm

📚 Current Electricity Easy

📋 Given Parameters & Problem Setup

Initial Cell EMF (E_1) 1.5 V

Initial Balancing Length (l_1) 36 cm

Replacement Cell EMF (E_2) 2.5 V

⚡

The 30-Second Exam Hall Shortcut: ⚡ Potentiometer Ratio Rule: l2 = l1 × (E2 / E1)

⏱️ Save ~20 seconds

Potential gradient is constant along the wire, so balancing length is strictly proportional to EMF: $l \propto E$ . Therefore, $l_2 = 36 \times \frac{2.5}{1.5} = 36 \times \frac{5}{3} = 12 \times 5 = 60\text{ cm}$ ! Instant 10-second calculation matching Option (1)!

1 Principle of potentiometer:

E \propto l \implies \frac{E_1}{E_2} = \frac{l_1}{l_2}

2 Express

l_2

l_2 = l_1 \left(\frac{E_2}{E_1}\right)

3 Substitute:

l_2 = 36\text{ cm} \times \left(\frac{2.5\text{ V}}{1.5\text{ V}}\right) = 36 \times \frac{5}{3}

l_2 = 60\text{ cm}

5 Match Option (1).

🛡️

Why You Can 100% Trust This Shortcut: Canonical potentiometer null deflection voltage-length proportionality.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Formulating the Principle of a Potentiometer

For a uniform potentiometer wire carrying a steady current, the potential drop per unit length (potential gradient $k$ ) is constant. At null deflection, the EMF of the test cell is balanced by the potential drop across balancing length $l$ :

E = k \cdot l \implies E \propto l

Step 2

Setting Up the Proportionality Ratio

Comparing the two test cells balanced on the same potentiometer wire:

\frac{E_1}{E_2} = \frac{l_1}{l_2} \implies l_2 = l_1 \left(\frac{E_2}{E_1}\right)

Step 3

Substituting Given Numerical Values

Substitute $l_1 = 36\text{ cm}$ , $E_1 = 1.5\text{ V}$ , and $E_2 = 2.5\text{ V}$ :

l_2 = 36\text{ cm} \times \frac{2.5}{1.5} = 36 \times \frac{5}{3} = 60\text{ cm}

⭐

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:

Exact balancing length for the 2.5 V cell: $36 \times (5/3) = 60\text{ cm}$ .

💡

Why this is airtight: None; textbook potentiometer derivation.

2 2

✗ Incorrect

Verdict & Scientific Reason:

Result of inverting the EMF ratio: $36 \times (1.5 / 2.5) = 21.6\text{ cm}$ (a higher EMF must produce a LARGER balancing length).

⚠️

Student Fallacy (Why candidates pick this trap): Inverting the ratio

E_1 / E_2

3 3

✗ Incorrect

Verdict & Scientific Reason:

Arithmetic approximation error.

⚠️

Student Fallacy (Why candidates pick this trap): Rough estimation without exact calculation.

4 4

✗ Incorrect

Verdict & Scientific Reason:

Calculation error.

⚠️

Student Fallacy (Why candidates pick this trap): Rounding error.

⚠️

NTA Trap Alert: Inverted Ratio Trap

Students who accidentally multiply by $E_1 / E_2$ obtain $21.6\text{ cm}$ , which NTA intentionally provided as Option (2). Since $2.5\text{ V} > 1.5\text{ V}$ , the balancing length MUST be longer than $36\text{ cm}$ .

🛡️ How to avoid the -1 mark: Sanity check: Larger EMF requires a LONGER length to balance.

l_2 > 36\text{ cm}

immediately eliminates Option (2).

📖

Core NEET Syllabus Standard

NCERT Physics · Current Electricity Standard Benchmark

Core Scientific Principle Tested:

"In a potentiometer circuit, balancing length is directly proportional to the cell EMF: $E_1 / E_2 = l_1 / l_2$ ."

Syllabus Focus: Potentiometer (Comparison of EMF of Two Cells)

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Physics Question 19 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Potentiometer Ratio Rule: l2 = l1 × (E2 / E1)

Step-by-Step Rigorous Workflow & Mathematical Proof

Formulating the Principle of a Potentiometer

Setting Up the Proportionality Ratio

Substituting Given Numerical Values

360° Option Elimination Engine Key Feature

NTA Trap Alert: Inverted Ratio 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

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