Q.47 Physics · Section B ⭐ 360° Option Elimination Active

NEET 2024 Physics Question 47 Solution

Topic: Electrostatic Potential and Capacitance · Official NTA Booklet Code T1

Question

If the plates of a parallel plate capacitor connected to a battery are moved close to each other, then A. the charge stored in it, increases. B. the energy stored in it, decreases. C. its capacitance increases. D. the ratio of charge to its potential remains the same. E. the product of charge and voltage increases. Choose the most appropriate answer from the options given below:

✓

Verified Against NTA Final Answer Key

Option (4) : A, C and E only

📚 Electrostatic Potential and Capacitance Easy

📋 Given Parameters & Problem Setup

Condition Capacitor remains connected to the battery (V = constant)

Action Plates are moved closer to each other (d decreases)

⚡

The 30-Second Exam Hall Shortcut: ⚡ Battery Connected (V = Const) Rule

⏱️ Save ~40 seconds

d decreases -> C = ε₀A/d INCREASES (C is true). V is constant -> Q = CV INCREASES (A is true). Q·V = CV² INCREASES (E is true). Energy U = ½CV² INCREASES (B is false) -> A, C and E only!

1 Battery connected means potential difference V is FIXED (V = const).

2 Plates moved closer: separation d decreases => Capacitance C = ε₀A/d INCREASES -> Statement C is TRUE.

3 Charge stored Q = CV: since C increases, Q INCREASES -> Statement A is TRUE.

4 Energy stored U = ½ C V²: since C increases and V is constant, U INCREASES (does NOT decrease) -> Statement B is FALSE.

5 Ratio of charge to potential Q/V = C: since C increases, this ratio INCREASES (does not remain same) -> Statement D is FALSE.

6 Product Q × V = C V²: INCREASES -> Statement E is TRUE.

7 Correct statements are A, C and E only -> Option (4) in under 15 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Parallel Plate Capacitor Dynamics at Constant Voltage (C = ε₀A/d, Q = CV, U = ½CV²).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Constant Potential Condition

Because the capacitor remains connected across the terminals of a battery throughout the operation, the potential difference V between its plates is held strictly constant by the battery EMF:

V = \text{constant}

Step 2

Analysis of Capacitance (Statement C)

Capacitance of a parallel plate capacitor with plate area A and separation d is given by C = ε₀A / d. When the plates are moved closer together, separation d decreases, which directly increases capacitance:

d \downarrow \implies C = \frac{\varepsilon_0 A}{d} \uparrow \quad (\text{Statement C is True})

Step 3

Analysis of Charge Stored (Statement A)

The charge Q stored on the plates is Q = C · V. With V held constant and C increasing, the battery supplies additional charge to the plates:

Q = C V \implies Q \uparrow \quad (\text{Statement A is True})

Step 4

Analysis of Stored Energy (Statement B)

The electrostatic potential energy U stored in the electric field of the capacitor is U = ½ C V². Since C increases and V is constant, stored energy increases:

U = \frac{1}{2} C V^2 \implies U \uparrow \quad (\text{Statement B is False})

Step 5

Analysis of Ratio Q / V (Statement D)

The ratio of charge to potential is the capacitance itself (Q/V = C). Since capacitance increases, the ratio changes and does not remain the same:

\frac{Q}{V} = C \ne \text{constant} \quad (\text{Statement D is False})

Step 6

Analysis of Product Q × V (Statement E)

The product of charge and voltage is Q · V = (CV) · V = C V². Because C increases and V is constant, the product increases:

Q \times V = C V^2 \uparrow \quad (\text{Statement E is True})

⭐

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:

Contains B and D, both of which are false statements.

⚠️

Student Fallacy (Why candidates pick this trap): Confusing battery-connected with battery-disconnected case.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Contains B, which is false.

⚠️

Student Fallacy (Why candidates pick this trap): Assuming energy decreases when plates are brought closer.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Contains B and omits C.

⚠️

Student Fallacy (Why candidates pick this trap): Overlooking the definition of capacitance.

4 (4)

✓ 100% Correct

Verdict & Scientific Reason:

All three statements A, C, and E are rigorously true under constant voltage.

💡

Why this is airtight: None.

⚠️

NTA Trap Alert: Battery Connected vs Disconnected Formula Swap

When battery is DISCONNECTED, Q is constant so U = Q²/(2C) decreases as C increases. Students use this formula here and erroneously think energy decreases.

🛡️ How to avoid the -1 mark: When battery remains CONNECTED, V is constant: use U = ½CV²! Since C increases, U MUST increase.

📖

Core NEET Syllabus Standard

Physics Core Electrostatics · Electrostatic Potential and Capacitance Standard Benchmark

Core Scientific Principle Tested:

"With battery connected, V remains constant; decreasing plate separation increases C, Q, and stored energy U."

Syllabus Focus: Capacitors and Capacitance Variation

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Battery on keeps Voltage neat: C, Q, and Energy all increase sweet (A, C, E)!

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NEET 2024 Physics Question 47 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Battery Connected (V = Const) Rule

Step-by-Step Rigorous Workflow & Mathematical Proof

Constant Potential Condition

Analysis of Capacitance (Statement C)

Analysis of Charge Stored (Statement A)

Analysis of Stored Energy (Statement B)

Analysis of Ratio Q / V (Statement D)

Analysis of Product Q × V (Statement E)

360° Option Elimination Engine Key Feature

NTA Trap Alert: Battery Connected vs Disconnected Formula Swap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Electrostatic Potential and Capacitance

Electrostatic Energy Ratio in a Series-Parallel Capacitor Network

Path-Independence of Electrostatic Work & Potential of a Uniformly Charged Sphere

Electrostatic Shielding and Cavity Field with Interior Point Charge

Speed of an Attracted Point Charge Reaching the Surface of a Charged Insulating Sphere

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