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NEET 2023 Physics Question 8 Solution

Topic: Alternating Current · Official NTA Booklet Code G5

Question

An ac source is connected to a capacitor C. Due to decrease in its operating frequency:

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Verified Against NTA Final Answer Key

Option (4) : displacement current decreases.

📚 Alternating Current Easy

📋 Given Parameters & Problem Setup

Circuit Element Capacitor C connected across AC source V

Condition Operating frequency f is decreased

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The 30-Second Exam Hall Shortcut: ⚡ Capacitive Ohm's Law and Conduction-Displacement Equality

⏱️ Save ~40 seconds

Lower frequency means higher capacitive reactance (X_C = 1/ωC ↑), so current drops (I = V/X_C ↓); displacement current equals conduction current, so it decreases!

1 Capacitive reactance formula: X_C = 1 / (2π f C). When frequency f decreases, X_C INCREASES.

2 Thus, options (1) and (2) claiming X_C remains constant or decreases are immediately FALSE.

3 Current in the circuit is I = V / X_C = V × (2π f C).

4 As f decreases, current I decreases.

5 By Maxwell-Ampere law, displacement current inside the dielectric equals conduction current in the leads (i_d = i_c = I).

6 Therefore, displacement current decreases. Pick Option (4)!

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Why You Can 100% Trust This Shortcut: Fundamental Electrodynamics · Maxwell-Ampere Law (Continuity of total current: i_c = i_d = C dV/dt ∝ f).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Capacitive Reactance Relation to Frequency

The opposition offered by a capacitor to alternating current is capacitive reactance X_C:

X_C = \frac{1}{\omega C} = \frac{1}{2\pi f C}

Step 2

Effect of Frequency Reduction on Reactance and Current

When the operating frequency f decreases, the capacitive reactance X_C increases inversely:

f \downarrow \implies X_C \uparrow

Step 3

Current and Displacement Current Relation

The alternating current in the circuit (conduction current i_c) is determined by Ohm's law in AC circuits:

i_c = \frac{V}{X_C} = V(2\pi f C) \implies i_c \propto f

Step 4

Maxwell's Displacement Current Equivalence

Inside the capacitor plates, the changing electric flux generates displacement current i_d, which identically equals the conduction current i_c at every instant:

i_d = \varepsilon_0 \frac{d\Phi_E}{dt} = i_c = V(2\pi f C)

Step 5

Conclusion

Since f decreases, i_d decreases proportionally:

f \downarrow \implies i_d \downarrow

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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:

False. X_C depends inversely on frequency (X_C = 1/(2πfC)).

⚠️

Student Fallacy (Why candidates pick this trap): Candidate confused capacitive reactance with ohmic resistance R (which is independent of frequency).

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

False. As frequency decreases, X_C increases, not decreases.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate confused capacitive reactance (1/ωC) with inductive reactance (X_L = ωL).

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

False. Since impedance increases, current decreases.

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Student Fallacy (Why candidates pick this trap): Candidate incorrectly thought reactance decrease leads to current increase.

4 (4)

✓ 100% Correct

Verdict & Scientific Reason:

Accurate deduction: lower frequency causes higher reactance, lowering both conduction and displacement currents.

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Why this is airtight: None. Candidate correctly applied i_d = i_c = V(2πfC).

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NTA Trap Alert: Confusing Displacement Current with a Constant Static Parameter

Some students treat displacement current as an abstract quantity separate from circuit current. In reality, i_d is continuous with conduction current i_c.

🛡️ How to avoid the -1 mark: Remember: i_d = i_c in any AC circuit across a capacitor. If circuit current drops, displacement current drops.

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Core NEET Syllabus Standard

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

Core Scientific Principle Tested:

"Capacitive current i = V/(X_C) = 2π f C V. Decreasing frequency reduces current directly."

Syllabus Focus: Capacitive AC Circuits and Displacement Current

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Physics Question 8 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Capacitive Ohm's Law and Conduction-Displacement Equality

Step-by-Step Rigorous Workflow & Mathematical Proof

Capacitive Reactance Relation to Frequency

Effect of Frequency Reduction on Reactance and Current

Current and Displacement Current Relation

Maxwell's Displacement Current Equivalence

Conclusion

360° Option Elimination Engine Key Feature

NTA Trap Alert: Confusing Displacement Current with a Constant Static Parameter

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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