Q.16 Physics ⭐ 360° Option Elimination Active

NEET 2025 Physics Question 16 Solution

Topic: Alternating Current · Official NTA Booklet Code 45

Question

To an ac power supply of 220 V at 50 Hz, a resistor of 20 Ω, a capacitor of reactance 25 Ω and an inductor of reactance 45 Ω are connected in series. The corresponding current in the circuit and the phase angle between the current and the voltage is, respectively

✓

Verified Against NTA Final Answer Key

Option (2) : 7.8 A and 45°

📚 Alternating Current Easy

📋 Given Parameters & Problem Setup

AC Supply Voltage (V_rms) 220 V at 50 Hz

Resistance (R) 20 Ω

Capacitive Reactance (X_C) 25 Ω

Inductive Reactance (X_L) 45 Ω

⚡

The 30-Second Exam Hall Shortcut: ⚡ 45° Isosceles Reactance Trap Rule

⏱️ Save ~45 seconds

X_L - X_C = 45 - 25 = 20 Ω = R ⟹ tan ϕ = 1 ⟹ ϕ = 45°! Z = R√2 = 20√2 Ω ⟹ I = 220 / (20√2) = 11 / 1.414 = 7.8 A!

1 Calculate net reactance: X = X_L - X_C = 45 - 25 = 20 Ω.

2 Notice: X = 20 Ω and R = 20 Ω. Because X = R, tan ϕ = X / R = 1 ⟹ ϕ = 45°!

3 This immediately eliminates options (1) & (3) which have 30°.

4 Impedance of isosceles right-angle triangle: Z = √(R² + X²) = 20√2 Ω.

5 RMS current: I_rms = V_rms / Z = 220 / (20√2) = 11 / √2 ≈ 7.78 A ≈ 7.8 A.

6 Match Option (2) in under 20 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Series LCR Resonance (NCERT Physics · Alternating Current: ω₀ = 1/√(LC)).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Compute Net Reactance and Circuit Impedance

In a series LCR circuit, inductive reactance leads the current while capacitive reactance lags by 90°. The net reactance is the algebraic difference:

X = X_L - X_C = 45\,\Omega - 25\,\Omega = 20\,\Omega

• Total impedance Z = √(R² + (X_L - X_C)²) = √(20² + 20²) = 20√2 Ω ≈ 28.28 Ω.

Step 2

Calculate RMS Current

The root-mean-square current supplied by the 220 V AC source is given by Ohm’s law for AC circuits:

I_{rms} = \frac{V_{rms}}{Z} = \frac{220\text{ V}}{20\sqrt{2}\,\Omega} = \frac{11}{\sqrt{2}}\text{ A} = \frac{11 \times 1.414}{2}\text{ A} \approx 7.78\text{ A} \approx 7.8\text{ A}

• Current is inductive (voltage leads current by phase angle ϕ).

Step 3

Determine the Phase Angle

The phase angle ϕ between voltage and current is determined from the impedance triangle:

\tan\phi = \frac{X_L - X_C}{R} = \frac{20\,\Omega}{20\,\Omega} = 1 \implies \phi = 45^\circ

• Thus the current is 7.8 A and the phase angle is 45°, corresponding to Option (2).

⭐

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 A

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Angle would be 30° only if tan ϕ = 1/√3; here tan ϕ = 20/20 = 1 ⟹ ϕ = 45°.

⚠️

Student Fallacy (Why candidates pick this trap): Confusing tan 30° with tan 45°.

2 B

✓ 100% Correct

Verdict & Scientific Reason:

100% exact. Z = 20√2 Ω ⟹ I = 11/√2 ≈ 7.8 A, and tan ϕ = 1 ⟹ ϕ = 45°.

💡

Why this is airtight: None; rigorous LCR analysis.

3 C

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. 15.6 A is obtained if peak current (I₀ = I_rms × √2 = 11 A × 1.414... wait, 220/14.14) is confused or impedance halved.

⚠️

Student Fallacy (Why candidates pick this trap): Doubling current or confusing RMS with peak value.

4 D

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. 15.6 A represents a factor-of-2 arithmetic error on current.

⚠️

Student Fallacy (Why candidates pick this trap): Using 220 / (R / 2) or arithmetic slip.

⚠️

NTA Trap Alert: Adding Reactances Instead of Subtracting

Students sometimes write Z = √(R² + (X_L + X_C)²), forgetting that inductor and capacitor reactances oppose each other in phase by 180°. Net reactance is ALWAYS X_L - X_C.

🛡️ How to avoid the -1 mark: Remember: L and C are in direct opposition: X_net = |X_L - X_C|.

📖

Core NEET Syllabus Standard

NEET Physics Core Syllabus · Alternating Current Standard Benchmark

Core Scientific Principle Tested:

"Impedance Z = √(R² + (X_L - X_C)²) and tan ϕ = (X_L - X_C) / R."

Syllabus Focus: Series LCR Circuit & Impedance

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Equal R and X ⟹ tan 45° = 1, and divide by √2 for current!

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NEET 2025 Physics Question 16 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ 45° Isosceles Reactance Trap Rule

Step-by-Step Rigorous Workflow & Mathematical Proof

Compute Net Reactance and Circuit Impedance

Calculate RMS Current

Determine the Phase Angle

360° Option Elimination Engine Key Feature

NTA Trap Alert: Adding Reactances Instead of Subtracting

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Alternating Current

Current Amplitude at Electrical Resonance in a Series LCR Circuit

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