Q.43 Physics · Section B ⭐ 360° Option Elimination Active

NEET 2024 Physics Question 43 Solution

Topic: Alternating Current · Official NTA Booklet Code T1

Question

A 10 μF capacitor is connected to a 210 V, 50 Hz source as shown in figure. The peak current in the circuit is nearly (π = 3.14):

✓

Verified Against NTA Final Answer Key

Option (4) : 0.93 A

📚 Alternating Current Medium

📋 Given Parameters & Problem Setup

Capacitance C = 10 μF = 10 × 10⁻⁶ F = 10⁻⁵ F

AC source voltage (RMS) V_rms = 210 V

Frequency f = 50 Hz

Value of π Take π = 3.14

⚡

The 30-Second Exam Hall Shortcut: ⚡ Peak Current Estimation Shortcut

⏱️ Save ~45 seconds

Peak current I₀ = V₀ ω C = (√2 × 210) × (2 × 3.14 × 50) × 10⁻⁵ = 297 × 314 × 10⁻⁵ ≈ 0.93 A!

1 Beware of the word "PEAK" current (not RMS current!): V₀ = √2 V_rms ≈ 1.414 × 210 ≈ 297 V.

2 Angular frequency: ω = 2πf = 2 × 3.14 × 50 = 314 rad/s.

3 Peak current: I₀ = V₀ / X_C = V₀ ω C.

4 Substitute: I₀ = 297 × 314 × 10⁻⁵ = 93,258 × 10⁻⁵ ≈ 0.9326 A ≈ 0.93 A.

5 Option (4) in under 25 seconds!

🛡️

Why You Can 100% Trust This Shortcut: AC Circuit Reactance and Peak Current Relations (I₀ = V₀ ω C = √2 V_rms 2πf C).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Calculation of Peak Voltage V₀

The voltage rating given for an AC power supply (210 V) represents its root-mean-square (RMS) voltage. The peak voltage V₀ is related to V_rms by:

V_0 = \sqrt{2} V_{rms} = 1.4142 \times 210\,\text{V} \approx 296.98\,\text{V}

Step 2

Calculation of Angular Frequency ω

For source frequency f = 50 Hz with π = 3.14:

\omega = 2\pi f = 2 \times 3.14 \times 50 = 314\,\text{rad/s}

Step 3

Formula for Capacitive Reactance X_C

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

X_C = \frac{1}{\omega C} = \frac{1}{314 \times 10^{-5}\,\text{F}} = \frac{10^5}{314} \approx 318.47\,\Omega

Step 4

Calculation of Peak Current I₀

The peak current I₀ in the pure capacitive circuit is:

I_0 = \frac{V_0}{X_C} = V_0 \omega C = (296.98\,\text{V}) \times (314\,\text{rad/s}) \times (10^{-5}\,\text{F})

Step 5

Numerical Evaluation

Multiplying the values:

I_0 = 93251.7 \times 10^{-5}\,\text{A} \approx 0.9325\,\text{A} \approx 0.93\,\text{A}

⭐

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:

Overestimates current.

⚠️

Student Fallacy (Why candidates pick this trap): Multiplying by an extra factor of √2.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Severe calculation error.

⚠️

Student Fallacy (Why candidates pick this trap): Using 60 Hz or dividing by incorrect factors.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Represents the RMS current I_rms (I_rms = 210 × 314 × 10⁻⁵ = 0.659 A, or with arithmetic error 0.58 A).

⚠️

Student Fallacy (Why candidates pick this trap): Calculating RMS current instead of PEAK current.

4 (4)

✓ 100% Correct

Verdict & Scientific Reason:

Exact evaluation of peak current I₀ = √2 V_rms ω C.

💡

Why this is airtight: None.

⚠️

NTA Trap Alert: Peak vs RMS Current Trap

Over 40% of students calculate I = V_rms / X_C = 210 × 314 × 10⁻⁵ ≈ 0.66 A, and hunt for an option near it, missing the keyword "PEAK current".

🛡️ How to avoid the -1 mark: Whenever you see "peak current", immediately multiply the rated voltage by √2: V₀ = √2 × 210 V.

📖

Core NEET Syllabus Standard

Physics Core Electrodynamics · Alternating Current Standard Benchmark

Core Scientific Principle Tested:

"In a capacitive AC circuit, peak current is I₀ = V₀ / X_C = V₀ ω C, where V₀ = √2 V_rms."

Syllabus Focus: AC Voltage Applied to a Capacitor

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Peak means multiply by Root 2: 297 times 314 gives 0.93 A true!

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NEET 2024 Physics Question 43 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Peak Current Estimation Shortcut

Step-by-Step Rigorous Workflow & Mathematical Proof

Calculation of Peak Voltage V₀

Calculation of Angular Frequency ω

Formula for Capacitive Reactance X_C

Calculation of Peak Current I₀

Numerical Evaluation

360° Option Elimination Engine Key Feature

NTA Trap Alert: Peak vs RMS Current Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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