Q.30 Physics ⭐ 360° Option Elimination Active

NEET 2026 Physics Question 30 Solution

Topic: Alternating Current · Official NTA Booklet Code 50

Question

An ac voltage V = 220 sin(2×10⁴ t) Volt is applied to a series LCR circuit. Then the current amplitude in this circuit is: (Given: L = 10 mH, C = 25 μF, R = 100 Ω)

✓

Verified Against NTA Final Answer Key

Option (1) : Current amplitude I_0 = 2.2 A

📚 Alternating Current Easy

📋 Given Parameters & Problem Setup

Applied Voltage V = 220 sin(2 * 10^3 t) V ==> V_0 = 220 V, omega = 2000 rad/s

Inductance L 10 mH = 10 * 10^-3 H = 0.01 H

Capacitance C 25 muF = 25 * 10^-6 F

Resistance R 100 Omega

Target Quantity Current amplitude (peak current I_0)

⚡

The 30-Second Exam Hall Shortcut: ⚡ Resonance Check in 10 Seconds

⏱️ Saves 90 seconds of complex impedance root-sum-square calculation.

Calculate X_L and X_C first: they are identical (Resonance)!

1 X_L = omega * L = (2000) * (0.01) = 20 Omega.

2 X_C = 1 / (omega * C) = 1 / (2000 * 25 * 10^-6) = 1 / (0.05) = 20 Omega.

3 X_L = X_C = 20 Omega ==> RESONANCE! Net reactance X = X_L - X_C = 0.

4 Total impedance Z = R = 100 Omega.

5 Current amplitude: I_0 = V_0 / Z = 220 V / 100 Omega = 2.2 A. Solved in 15 seconds!

🛡️

Why You Can 100% Trust This Shortcut: At resonance, inductive and capacitive reactances cancel out completely (180 degrees out of phase), making circuit impedance purely resistive: Z = R.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Extract AC Voltage Parameters

Comparing the given equation V = 220 \sin(2 \times 10^3 t) with standard AC form V = V_0 \sin(\omega t):

V_0 = 220\text{ V}, \qquad \omega = 2 \times 10^3\text{ rad/s} = 2000\text{ rad/s}

• V_0 is the peak voltage amplitude.
• omega is the angular frequency.

Step 2

Calculate Inductive and Capacitive Reactances

Compute reactances of inductor L and capacitor C:

X_L = \omega L = 2000 \times (10 \times 10^{-3}) = 20\,\Omega, \qquad X_C = \frac{1}{\omega C} = \frac{1}{2000 \times (25 \times 10^{-6})} = \frac{10^6}{50000} = 20\,\Omega

• Because X_L = X_C = 20 Omega, the circuit operates at its exact resonant frequency.
• Net reactance is zero: X_L - X_C = 0.

Step 3

Calculate Circuit Impedance and Current Amplitude

Impedance of a series LCR circuit:

Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{100^2 + 0} = 100\,\Omega

• Current amplitude (peak current) is:
• I_0 = \frac{V_0}{Z} = \frac{220\text{ V}}{100\,\Omega} = 2.2\text{ A}.
• Matches Option (1) exactly.

⭐

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)

✓ 100% Correct

Verdict & Scientific Reason:

100% mathematically exact; confirmed by Official NTA Final Answer Key.

💡

Why this is airtight: Correctly identifies resonance and evaluates I_0 = V_0 / R = 220 / 100 = 2.2 A.

Note: Flawless execution.

2 Option (2)

✗ Incorrect

Verdict & Scientific Reason:

Uses net reactance as impedance.

⚠️

Student Fallacy (Why candidates pick this trap): Divides 220 by 40 (sum of reactances).

Note: Reactances cancel at resonance; they do not add.

3 Option (3)

✗ Incorrect

Verdict & Scientific Reason:

Uses 20 Omega reactance alone as impedance.

⚠️

Student Fallacy (Why candidates pick this trap): Calculates 220 / 20 = 11.0 A, ignoring the resistor.

Note: Resistor R = 100 Omega is the sole remaining impedance.

4 Option (4)

✗ Incorrect

Verdict & Scientific Reason:

Power-of-ten arithmetic error.

⚠️

Student Fallacy (Why candidates pick this trap): Uses R = 10 Omega instead of 100 Omega.

Note: R is given as 100 Omega.

⚠️

NTA Trap Alert: Confusing Current Amplitude with RMS Current

Students who divide by sqrt(2) compute I_rms = 2.2 / 1.414 = 1.55 A and wonder why it is missing.

🛡️ How to avoid the -1 mark: Always note the wording: "current amplitude" means PEAK current I_0 = V_0 / Z. If "rms current" were asked, it would use V_rms.

📖

Core NEET Syllabus Standard

NEET UG Physics Core Standards · Alternating Current Standard Benchmark

Core Scientific Principle Tested:

"At resonance, omega*L = 1/(omega*C), net reactance vanishes, impedance is minimum Z = R, and current amplitude reaches maximum I_0 = V_0 / R."

Syllabus Focus: Series LCR Circuit & Resonance Phenomenon

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2026 Physics Question 30 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Resonance Check in 10 Seconds

Step-by-Step Rigorous Workflow & Mathematical Proof

Extract AC Voltage Parameters

Calculate Inductive and Capacitive Reactances

Calculate Circuit Impedance and Current Amplitude

360° Option Elimination Engine Key Feature

NTA Trap Alert: Confusing Current Amplitude with RMS Current

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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