Q.5 Physics ⭐ 360° Option Elimination Active

NEET 2023 Physics Question 5 Solution

Topic: Alternating Current · Official NTA Booklet Code G5

Question

In a series LCR circuit, the inductance L is 10 mH, capacitance C is 1 μF and resistance R is 100 Ω. The frequency at which resonance occurs is:

✓

Verified Against NTA Final Answer Key

Option (1) : 1.59 kHz

📚 Alternating Current Easy

📋 Given Parameters & Problem Setup

Inductance (L) 10 mH = 10 × 10⁻³ H = 10⁻² H

Capacitance (C) 1 μF = 1 × 10⁻⁶ F

Resistance (R) 100 Ω (independent of resonant frequency)

⚡

The 30-Second Exam Hall Shortcut: ⚡ LC Product Decimal Shortcut with 1/(2π) ≈ 0.159

⏱️ Save ~45 seconds

LC = 10⁻² × 10⁻⁶ = 10⁻⁸ → √LC = 10⁻⁴ → f₀ = 10⁴ / (2π) = 0.159 × 10⁴ Hz = 1.59 kHz in 15 seconds!

1 Compute LC: (10 × 10⁻³) × (10⁻⁶) = 10⁻⁸ s².

2 Take square root: √(LC) = 10⁻⁴ s.

3 Resonant frequency in Hz is f₀ = 1 / [2π √(LC)] = 10⁴ / (2π).

4 Use the constant memory hook: 1 / (2π) ≈ 0.159.

5 0.159 × 10⁴ Hz = 1590 Hz ≈ 1.59 kHz. Immediately select Option (1)!

🛡️

Why You Can 100% Trust This Shortcut: Fundamental AC Theory · Resonant Circuits (Series resonance condition: X_L = X_C → ω₀ = 1/√(LC) and f₀ = 1/(2π√(LC))).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Condition for Electrical Resonance in Series LCR

Resonance in a series LCR circuit occurs when inductive reactance equals capacitive reactance, causing impedance to become purely resistive (Z = R):

X_L = X_C \implies \omega_0 L = \frac{1}{\omega_0 C} \implies \omega_0^2 = \frac{1}{LC} \implies \omega_0 = \frac{1}{\sqrt{LC}}

Step 2

Calculation of Angular Frequency ω₀

Substitute inductance L = 10 × 10⁻³ H and capacitance C = 10⁻⁶ F:

\omega_0 = \frac{1}{\sqrt{(10 \times 10^{-3}) \times (10^{-6})}} = \frac{1}{\sqrt{10^{-8}}} = \frac{1}{10^{-4}} = 10^4\text{ rad/s}

Step 3

Conversion from Angular Frequency to Linear Frequency in Hertz

Convert angular frequency ω₀ (in rad/s) to cyclic frequency f₀ (in Hz):

f_0 = \frac{\omega_0}{2\pi} = \frac{10^4}{2 \times 3.1416} = \frac{10000}{6.2832} \approx 1591.5\text{ Hz} = 1.59\text{ kHz}

⭐

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)

✓ 100% Correct

Verdict & Scientific Reason:

Accurate value of linear frequency f₀ in kilohertz.

💡

Why this is airtight: None. Candidate correctly divided by 2π to get Hertz rather than rad/s.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Wrong unit and wrong magnitude (angular frequency is 10,000 rad/s).

⚠️

Student Fallacy (Why candidates pick this trap): Candidate mixed up orders of magnitude and mistakenly labelled cyclic frequency with rad/s.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Off by a factor of 10.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate calculated 10⁵ instead of 10⁴ during square root inversion.

4 (4)

✗ Incorrect

Verdict & Scientific Reason:

Gross unit mismatch and incorrect numerical magnitude.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate divided by 2π but retained rad/s units.

⚠️

NTA Trap Alert: Cyclic Frequency (Hz) vs Angular Frequency (rad/s)

NTA includes both units (kHz and rad/s) among the choices. If a student forgets to divide ω by 2π, they will search for 10⁴ rad/s and get confused.

🛡️ How to avoid the -1 mark: Whenever "frequency" is asked without the word "angular", calculate f in Hertz (divide by 2π).

📖

Core NEET Syllabus Standard

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

Core Scientific Principle Tested:

"Resonant frequency f₀ = 1 / (2π √LC) depends solely on L and C, completely independent of resistance R."

Syllabus Focus: Resonance in Series LCR Circuits

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Physics Question 5 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ LC Product Decimal Shortcut with 1/(2π) ≈ 0.159

Step-by-Step Rigorous Workflow & Mathematical Proof

Condition for Electrical Resonance in Series LCR

Calculation of Angular Frequency ω₀

Conversion from Angular Frequency to Linear Frequency in Hertz

360° Option Elimination Engine Key Feature

NTA Trap Alert: Cyclic Frequency (Hz) vs Angular Frequency (rad/s)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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