Q.9 Physics ⭐ 360° Option Elimination Active

NEET 2026 Physics Question 9 Solution

Topic: Electrostatics & Capacitors · Official NTA Booklet Code 50

Question

Three identical capacitors P, Q and S, each of the capacitance C, are connected to a battery of voltage V, as shown in the figure. If the energy stored in the capacitor P and total energy stored in the system are U_P and U_T, respectively, then the ratio U_P/U_T is:

✓

Verified Against NTA Final Answer Key

Option (4) : Ratio U_P / U_T = 1/6

📚 Electrostatics & Capacitors Medium

📋 Given Parameters & Problem Setup

Capacitors P, Q, S Three identical capacitors of capacitance C

Branch 1 Capacitors P and Q connected in series across battery V

Branch 2 Capacitor S connected in parallel across battery V

Target Ratio U_P / U_T (Energy in P / Total system energy)

⚡

The 30-Second Exam Hall Shortcut: ⚡ Voltage-Squared Unit Energy Method

⏱️ Bypasses lengthy equivalent capacitance derivations.

Assign unit energy u_0 = (1/2)*C*V^2 to a capacitor directly across V

1 Capacitor S is directly across voltage V: Stored energy U_S = (1/2)*C*V^2 = 1 unit.

2 Capacitors P and Q are identical in series across V, so voltage across each is V/2.

3 Energy in P: U_P = (1/2)*C*(V/2)^2 = (1/4) of a unit.

4 Energy in Q: U_Q = (1/4) of a unit.

5 Total system energy U_T = U_P + U_Q + U_S = 1/4 + 1/4 + 1 = 3/2 = 6/4 units.

6 Ratio U_P / U_T = (1/4) / (6/4) = 1/6. Solved in 20 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Energy stored in any capacitor is U = (1/2)*C*V_cap^2. In a series string of N identical capacitors across V, each gets V/N and stores 1/N^2 the energy of a single parallel unit.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Calculate Energy Stored in Capacitor P

Capacitors P and Q are connected in series across the battery voltage V. Since they have identical capacitance C, the battery voltage divides equally across them:

V_P = \frac{V}{2} \implies U_P = \frac{1}{2} C V_P^2 = \frac{1}{2} C \left(\frac{V}{2}\right)^2 = \frac{1}{8} C V^2

• Capacitor Q also stores exactly U_Q = (1/8) * C * V^2.

Step 2

Calculate Energy Stored in Capacitor S and Total Energy U_T

Capacitor S is connected in parallel directly across the battery terminals, experiencing the full potential difference V:

U_S = \frac{1}{2} C V^2 = \frac{4}{8} C V^2

• Total energy stored in the entire system is the sum of energies in all three capacitors:
• U_T = U_P + U_Q + U_S = \frac{1}{8}CV^2 + \frac{1}{8}CV^2 + \frac{4}{8}CV^2 = \frac{6}{8}CV^2 = \frac{3}{4}CV^2.

Step 3

Calculate the Energy Ratio U_P / U_T

Divide the energy stored in P by the total system energy:

\frac{U_P}{U_T} = \frac{\frac{1}{8} C V^2}{\frac{6}{8} C V^2} = \frac{1}{6}

• The factor C * V^2 cancels cleanly.
• Leaves the exact fraction 1/6, matching Option (4).

⭐

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 Option (1)

✗ Incorrect

Verdict & Scientific Reason:

Inverted logic.

⚠️

Student Fallacy (Why candidates pick this trap): Takes the ratio of equivalent capacitances without squaring the branch voltages.

Note: Energy scales with voltage squared, not linearly.

2 Option (2)

✗ Incorrect

Verdict & Scientific Reason:

Equal partition misconception.

⚠️

Student Fallacy (Why candidates pick this trap): Assumes the three capacitors share total energy equally (1/3 each), ignoring that S has twice the voltage of P.

Note: S is in parallel and holds four times the energy of P.

3 Option (3)

✗ Incorrect

Verdict & Scientific Reason:

Ignores capacitor S entirely.

⚠️

Student Fallacy (Why candidates pick this trap): Computes U_P / (U_P + U_Q) = (1/8) / (2/8) = 1/2, forgetting the parallel capacitor S.

Note: Total system energy U_T includes all three capacitors.

4 Option (4)

✓ 100% Correct

Verdict & Scientific Reason:

100% verified and confirmed by Official NTA Final Answer Key.

💡

Why this is airtight: Correctly squares the halved voltage on P and sums all three components: (1/8) / (6/8) = 1/6.

Note: Exact physics.

⚠️

NTA Trap Alert: The "Equal Energy Partition" Fallacy

Students often assume three identical capacitors mean each has 1/3 of the energy, marking Option (2).

🛡️ How to avoid the -1 mark: Always find the actual potential difference across each capacitor first: U = (1/2)*C*V_actual^2.

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Core NEET Syllabus Standard

NEET UG Physics Core Standards · Electrostatic Potential and Capacitance Standard Benchmark

Core Scientific Principle Tested:

"Total energy in any capacitor network is the scalar sum of individual stored energies: U_total = sum((1/2)*C_i*V_i^2)."

Syllabus Focus: Energy Stored in Capacitor Combinations

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2026 Physics Question 9 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Voltage-Squared Unit Energy Method

Step-by-Step Rigorous Workflow & Mathematical Proof

Calculate Energy Stored in Capacitor P

Calculate Energy Stored in Capacitor S and Total Energy U_T

Calculate the Energy Ratio U_P / U_T

360° Option Elimination Engine Key Feature

NTA Trap Alert: The "Equal Energy Partition" Fallacy

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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