Q.41 Physics ⭐ 360° Option Elimination Active

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NEET 2023 Physics Question 41 Solution

Topic: Alternating Current · Official NTA Booklet Code G5

Question

The net impedance of circuit (as shown in figure) will be:

✓

Verified Against NTA Final Answer Key

Option (4) : 5√5 Ω

📚 Alternating Current Medium

📋 Given Parameters & Problem Setup

Inductance (L) (50 / π) mH = (50 / π) × 10⁻³ H

Capacitance (C) (10³ / π) μF = (10³ / π) × 10⁻⁶ F = 10⁻³ / π F

Resistance (R) 10 Ω

AC Supply frequency (f) 50 Hz

⚡

The 30-Second Exam Hall Shortcut: ⚡ π Cancellation Hack: ω = 2π(50) = 100π rad/s

⏱️ Save ~50 seconds

X_L = (100π)(50/π × 10⁻³) = 5 Ω. X_C = 1 / [(100π)(10⁻³/π)] = 10 Ω. Net reactance |X_L - X_C| = 5 Ω. Impedance Z = √(10² + 5²) = √125 = 5√5 Ω in 25 seconds!

1 Angular frequency ω = 2π f = 2π(50) = 100π rad/s.

2 Inductive reactance: X_L = ω L = (100π) × [(50/π) × 10⁻³] = 100 × 50 × 10⁻³ = 5 Ω (π cancels!).

3 Capacitive reactance: X_C = 1 / (ω C) = 1 / [100π × (10⁻³/π)] = 1 / (100 × 10⁻³) = 1 / 0.1 = 10 Ω (π cancels!).

4 Net reactance: |X_L - X_C| = |5 - 10| = 5 Ω.

5 Net impedance: Z = √(R² + (X_L - X_C)²) = √(10² + 5²) = √(100 + 25) = √125 = 5√5 Ω.

6 Lock Option (4) 5√5 Ω immediately!

🛡️

Why You Can 100% Trust This Shortcut: Alternating Current · Series LCR Circuit Phasor Analysis (Z = √(R² + (X_L - X_C)²), where X_L = ωL and X_C = 1/(ωC)).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Determination of Angular Frequency ω

For an AC voltage source operating at a linear frequency of f = 50 Hz, the angular frequency ω is given by:

\omega = 2\pi f = 2\pi (50) = 100\pi\text{ rad s}^{-1}

Step 2

Calculation of Inductive Reactance (X_L)

Substitute inductance L = (50/π) mH = (50/π) × 10⁻³ H into the inductive reactance formula:

X_L = \omega L = (100\pi) \times \left(\frac{50}{\pi} \times 10^{-3}\right) = 100 \times 50 \times 10^{-3} = 5\ \Omega

Step 3

Calculation of Capacitive Reactance (X_C)

Substitute capacitance C = (10³/π) μF = (10⁻³/π) F into the capacitive reactance formula:

X_C = \frac{1}{\omega C} = \frac{1}{(100\pi) \times \left(\frac{10^{-3}}{\pi}\right)} = \frac{1}{100 \times 10^{-3}} = \frac{1}{0.1} = 10\ \Omega

Step 4

Phasor Combination to Determine Net Impedance (Z)

In a series LCR circuit, resistance and net reactance combine orthogonally in the impedance triangle:

Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{10^2 + (5 - 10)^2} = \sqrt{100 + (-5)^2} = \sqrt{100 + 25} = \sqrt{125} = 5\sqrt{5}\ \Omega

⭐

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:

Scalar sum of R + X_L + X_C (10 + 5 + 10 = 25 Ω).

⚠️

Student Fallacy (Why candidates pick this trap): Candidate treated components as simple DC resistors, ignoring phase angles.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Result if net reactance were equal to resistance (10 Ω).

⚠️

Student Fallacy (Why candidates pick this trap): Candidate calculated Z = √(10² + 10²) assuming X_L = 0.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Scalar addition of R and |X_L - X_C| (10 + 5 = 15 Ω).

⚠️

Student Fallacy (Why candidates pick this trap): Candidate added resistance and reactance linearly without Pythagoras’ theorem.

4 (4)

✓ 100% Correct

Verdict & Scientific Reason:

Accurate impedance: √(10² + 5²) = √125 = 5√5 Ω.

💡

Why this is airtight: None. Candidate executed phasor impedance calculation flawlessly.

⚠️

NTA Trap Alert: Linear Addition of Reactance and Resistance (Choosing 15 Ω or 25 Ω)

Voltages across resistors, inductors, and capacitors are out of phase by 90°. Adding them as DC resistances (10 + 5 = 15 Ω or 10 + 5 + 10 = 25 Ω) is completely incorrect. Impedance requires phasor summation: Z = √(R² + (X_L - X_C)²).

🛡️ How to avoid the -1 mark: Always construct the impedance triangle: Z² = R² + X_net².

📖

Core NEET Syllabus Standard

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

Core Scientific Principle Tested:

"Impedance is given by Z = √(R² + (X_L - X_C)²), where reactances subtract due to opposite 180° phase difference."

Syllabus Focus: Series LCR Circuit and Impedance

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Physics Question 41 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ π Cancellation Hack: ω = 2π(50) = 100π rad/s

Step-by-Step Rigorous Workflow & Mathematical Proof

Determination of Angular Frequency ω

Calculation of Inductive Reactance (X_L)

Calculation of Capacitive Reactance (X_C)

Phasor Combination to Determine Net Impedance (Z)

360° Option Elimination Engine Key Feature

NTA Trap Alert: Linear Addition of Reactance and Resistance (Choosing 15 Ω or 25 Ω)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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