Q.20 Physics ⭐ 360° Option Elimination Active

NEET 2025 Physics Question 20 Solution

Topic: Electrostatic Potential and Capacitance · Official NTA Booklet Code 45

Question

The plates of a parallel plate capacitor are separated by d. Two slabs of different dielectric constant K₁ and K₂ with thickness 3d/8 and d/2, respectively are inserted in the capacitor. Due to this, the capacitance becomes two times larger than when there is nothing between the plates. If K₁ = 1.25 K₂, the value of K₁ is:

✓

Verified Against NTA Final Answer Key

Option (1) : 2.66

📚 Electrostatic Potential and Capacitance Medium

📋 Given Parameters & Problem Setup

Plate Separation d

Slab 1 Thickness & Dielectric t₁ = (3/8) d, constant K₁

Slab 2 Thickness & Dielectric t₂ = d / 2 = (4/8) d, constant K₂

Capacitance Boost C = 2 C₀ (twice the air-filled capacitance)

Dielectric Ratio K₁ = 1.25 K₂ = (5/4) K₂

⚡

The 30-Second Exam Hall Shortcut: ⚡ Effective Separation Inversion Trick

⏱️ Save ~60 seconds

Air gap = d - (3/8 + 4/8)d = d/8. C = 2 C₀ ⟹ 3/(8K₁) + 4/(8K₂) + 1/8 = 1/2 ⟹ 3/K₁ + 4/K₂ = 3 ⟹ With K₂ = 4K₁/5: 8/K₁ = 3 ⟹ K₁ = 8/3 = 2.66!

1 Calculate remaining air gap: t_air = d - 3d/8 - 4d/8 = d/8.

2 Effective separation formula: d_eff = t₁/K₁ + t₂/K₂ + t_air = d [ 3/(8K₁) + 4/(8K₂) + 1/8 ].

3 Since C = 2 C₀, d_eff must equal d / 2 ⟹ 3/(8K₁) + 4/(8K₂) + 1/8 = 1/2.

4 Subtract 1/8: 3/(8K₁) + 4/(8K₂) = 3/8 ⟹ 3/K₁ + 4/K₂ = 3.

5 Substitute K₂ = 4K₁ / 5: 3/K₁ + 4 / (4K₁/5) = 3/K₁ + 5/K₁ = 8/K₁ = 3.

6 K₁ = 8 / 3 ≈ 2.66.

7 Select Option (1) in under 30 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Parallel Plate Capacitance with Dielectric Slab (NCERT Physics · Electrostatic Potential and Capacitance: C = ε₀A / (d - t + t/K)).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Effective Separation for Composite Dielectrics

For a parallel plate capacitor of area A and plate separation d containing dielectric slabs in series, the capacitance is:

C = \frac{\varepsilon_0 A}{\sum \frac{t_i}{K_i}} = \frac{\varepsilon_0 A}{\frac{t_1}{K_1} + \frac{t_2}{K_2} + t_{air}}

• t₁ = (3/8) d, t₂ = (1/2) d = (4/8) d.
• Air gap thickness: t_air = d - (3/8 d + 4/8 d) = (1/8) d.

Step 2

Set up the Capacitance Doubling Condition

The problem states that C = 2 C₀, where C₀ = ε₀ A / d:

\frac{\varepsilon_0 A}{\frac{3d}{8 K_1} + \frac{4d}{8 K_2} + \frac{d}{8}} = 2 \left(\frac{\varepsilon_0 A}{d}\right) \implies \frac{3}{8 K_1} + \frac{4}{8 K_2} + \frac{1}{8} = \frac{1}{2}

• Subtract 1/8 from both sides: 3/(8 K₁) + 4/(8 K₂) = 1/2 - 1/8 = 3/8.
• Multiplying throughout by 8 gives the simplified linear form: 3/K₁ + 4/K₂ = 3.

Step 3

Substitute K₁ = 1.25 K₂ and Solve for K₁

Given K₁ = 1.25 K₂ = (5/4) K₂, which implies K₂ = (4/5) K₁:

\frac{3}{K_1} + \frac{4}{\frac{4}{5} K_1} = 3 \implies \frac{3}{K_1} + \frac{5}{K_1} = 3 \implies \frac{8}{K_1} = 3 \implies K_1 = \frac{8}{3} \approx 2.666... = 2.66

• Matches Option (1) with absolute precision.

⭐

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

✓ 100% Correct

Verdict & Scientific Reason:

100% correct. K₁ = 8/3 ≈ 2.66.

💡

Why this is airtight: None; rigorous algebraic derivation.

2 B

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Occurs if the air gap (d/8) is neglected.

⚠️

Student Fallacy (Why candidates pick this trap): Forgetting the leftover air gap between the two slabs.

3 C

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Solving for K₂ gives K₂ = 4/5 × (8/3) = 32/15 ≈ 2.13, not 1.60.

⚠️

Student Fallacy (Why candidates pick this trap): Arithmetic misstep during ratio substitution.

4 D

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Corresponds to 4/3 instead of 8/3.

⚠️

Student Fallacy (Why candidates pick this trap): Dropping a factor of 2 in numerator (4/K₁ = 3).

⚠️

NTA Trap Alert: The Forgotten Air Gap (d/8)

Students frequently sum the thicknesses 3d/8 + d/2 = 7d/8 and assume the slabs fill the ENTIRE capacitor! The missing 1/8 d is an air gap (K = 1). Ignoring it leads to completely wrong dielectric constants.

🛡️ How to avoid the -1 mark: Always check: Does Σ t_i equal d? 3/8 + 4/8 = 7/8 ≠ 1 ⟹ leftover air gap = 1/8 d!

📖

Core NEET Syllabus Standard

NEET Physics Core Syllabus · Electrostatic Potential and Capacitance Standard Benchmark

Core Scientific Principle Tested:

"Effective separation is d_eff = Σ (t_i / K_i). Air gap corresponds to K = 1."

Syllabus Focus: Capacitors with Multiple Dielectric Slabs

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

3/8 + 4/8 leaves 1/8 air gap ⟹ 3/K₁ + 5/K₁ = 3 ⟹ K₁ = 8/3 = 2.66!

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NEET 2025 Physics Question 20 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Effective Separation Inversion Trick

Step-by-Step Rigorous Workflow & Mathematical Proof

Effective Separation for Composite Dielectrics

Set up the Capacitance Doubling Condition

Substitute K₁ = 1.25 K₂ and Solve for K₁

360° Option Elimination Engine Key Feature

NTA Trap Alert: The Forgotten Air Gap (d/8)

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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