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NEET 2023 Physics Question 10 Solution

Topic: Current Electricity · Official NTA Booklet Code G5

Question

If the galvanometer G does not show any deflection in the circuit shown, the value of R is given by:

✓

Verified Against NTA Final Answer Key

Option (4) : 100 Ω

📚 Current Electricity Easy

📋 Given Parameters & Problem Setup

Primary Battery 10 V

Series Primary Resistor 400 Ω

Secondary Null-Balance Battery 2 V

Condition Galvanometer G shows zero deflection (i_g = 0)

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The 30-Second Exam Hall Shortcut: ⚡ Voltage Divider Ratio Mental Shortcut

⏱️ Save ~45 seconds

Zero deflection means voltage across R is exactly 2 V! The 10 V battery splits into 8 V across 400 Ω and 2 V across R. Since 2 V is 1/4th of 8 V, R = 400/4 = 100 Ω in 10 seconds!

1 Null deflection (i_g = 0) means no current enters the galvanometer branch.

2 Therefore, the voltage across resistor R must exactly equal the secondary battery: V_R = 2 V.

3 Since total supply is 10 V, the remaining voltage across the 400 Ω resistor is 10 - 2 = 8 V.

4 By simple proportion of series resistors: R / 400 = V_R / V_400 = 2 / 8 = 1 / 4.

5 R = 400 / 4 = 100 Ω. Instantly pick Option (4)!

🛡️

Why You Can 100% Trust This Shortcut: Fundamental DC Circuit Theory · Kirchhoff's Laws & Voltage Division (Series voltage divider ratio: V₁/V₂ = R₁/R₂).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Significance of Null Deflection in Galvanometer Branch

When the galvanometer G shows zero deflection, the current flowing through its branch is zero (i_g = 0). By Kirchhoff's Current Law at the junction, the secondary branch is completely isolated in terms of current flow:

i_g = 0 \implies V_R = 2\text{ V}

Step 2

Current in the Primary Series Loop

All current from the 10 V source circulates exclusively through the series combination of 400 Ω and R:

I = \frac{10}{400 + R}

Step 3

Voltage Balance across Resistor R

The potential drop across resistor R is given by Ohm's law and must balance the 2 V battery:

V_R = I \times R = \left(\frac{10}{400 + R}\right) R = 2\text{ V}

Step 4

Algebraic Solution for R

Solve the linear equation for resistance R:

10 R = 2(400 + R) \implies 10 R = 800 + 2 R \implies 8 R = 800 \implies R = 100\ \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:

If R were 400 Ω, V_R would be 5 V (half of 10 V), creating a 3 V unbalance across the 2 V cell.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate assumed symmetrical resistance division (R = 400 Ω).

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

If R were 200 Ω, V_R = (200/600) × 10 = 3.33 V ≠ 2 V.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate incorrectly multiplied 100 Ω by 2.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

If R were 50 Ω, V_R = (50/450) × 10 = 1.11 V ≠ 2 V.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate made an arithmetic division slip, dividing 100 Ω by 2.

4 (4)

✓ 100% Correct

Verdict & Scientific Reason:

Accurate value producing exact 2 V drop across R to achieve galvanometer null deflection.

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Why this is airtight: None. Candidate correctly applied the potentiometer balance condition.

⚠️

NTA Trap Alert: Applying Wheatstone Bridge Formula in an Unrelated Two-Battery Loop

Some students attempt to treat this circuit as a Wheatstone bridge and search for four ratio arms. This is simply a potentiometer-style null balance circuit.

🛡️ How to avoid the -1 mark: Whenever a galvanometer has a battery in series and shows zero deflection, set the node voltage equal to that battery voltage!

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Core NEET Syllabus Standard

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

Core Scientific Principle Tested:

"At null balance (i = 0), the branch draws no current and the terminal potential difference across the parallel resistor equals the secondary EMF."

Syllabus Focus: Kirchhoff's Laws and Null Deflection Circuit Analysis

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Physics Question 10 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Voltage Divider Ratio Mental Shortcut

Step-by-Step Rigorous Workflow & Mathematical Proof

Significance of Null Deflection in Galvanometer Branch

Current in the Primary Series Loop

Voltage Balance across Resistor R

Algebraic Solution for R

360° Option Elimination Engine Key Feature

NTA Trap Alert: Applying Wheatstone Bridge Formula in an Unrelated Two-Battery Loop

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

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