Q.50 Physics ⭐ 360° Option Elimination Active

NEET 2021 Physics Question 50 Solution

Topic: Alternating Current · Official NTA Booklet Code M1

Question

A step down transformer connected to an ac mains supply of 220 V is made to operate at 11 V, 44 W lamp. Ignoring power losses in the transformer, what is the current in the primary circuit?

✓

Verified Against NTA Final Answer Key

Option (1) : 0.2 A

📚 Alternating Current Easy

📋 Given Parameters & Problem Setup

Primary Supply Voltage (V_p) 220 V

Secondary Operating Voltage (V_s) 11 V

Lamp Rated Power (P_s) 44 W

Efficiency Condition Ideal transformer (losses ignored, 100% efficiency)

⚡

The 30-Second Exam Hall Shortcut: ⚡ Conservation of Power: P_primary = P_secondary

⏱️ Save ~20 seconds

For an ideal lossless transformer, input power equals output power: $P_p = P_s = 44\text{ W}$ . Since $P_p = V_p I_p$ , we immediately have $I_p = \frac{P_s}{V_p} = \frac{44\text{ W}}{220\text{ V}} = \frac{4}{20} = 0.2\text{ A}$ ! Instant 5-second calculation matching Option (1)!

1 Lossless transformer

\implies

Input Power = Output Power:

V_p I_p = P_{\text{out}}

2 Secondary lamp operates at rated power:

P_{\text{out}} = 44\text{ W}

3 Substitute primary voltage

V_p = 220\text{ V}

220 \times I_p = 44

4 Primary current:

I_p = \frac{44}{220} = \frac{1}{5} = 0.2\text{ A}

5 Match Option (1).

🛡️

Why You Can 100% Trust This Shortcut: Canonical conservation of electrical energy for ideal mutual transformers.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Formulating the Ideal Transformer Power Equality

In an ideal transformer, eddy current, hysteresis, and copper winding losses are completely neglected. By conservation of electrical energy, the power delivered to the primary circuit equals the power consumed by the load in the secondary circuit:

P_p = P_s \implies V_p I_p = V_s I_s = P_{\text{lamp}}

Step 2

Calculating the Primary Current (I_p)

The lamp consumes $P_s = 44\text{ W}$ at primary voltage $V_p = 220\text{ V}$ . Rearranging for primary current:

I_p = \frac{P_s}{V_p} = \frac{44\text{ W}}{220\text{ V}} = \frac{44}{220}\text{ A} = \frac{1}{5}\text{ A} = 0.2\text{ A}

Step 3

Verifying via Turns Ratio and Secondary Current

Secondary current is $I_s = \frac{P_s}{V_s} = \frac{44\text{ W}}{11\text{ V}} = 4\text{ A}$ . The turns ratio is $\frac{V_s}{V_p} = \frac{11}{220} = \frac{1}{20}$ . By current transformation ratio:

I_p = I_s \left(\frac{V_s}{V_p}\right) = 4\text{ A} \times \left(\frac{1}{20}\right) = 0.2\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

✓ 100% Correct

Verdict & Scientific Reason:

Exact primary current: $I_p = 44\text{ W} / 220\text{ V} = 0.2\text{ A}$ .

💡

Why this is airtight: None; textbook transformer calculation.

2 2

✗ Incorrect

Verdict & Scientific Reason:

Result of an arithmetic doubling error.

⚠️

Student Fallacy (Why candidates pick this trap): Dividing 44 by 110 instead of 220.

3 3

✗ Incorrect

Verdict & Scientific Reason:

Off by a factor of 10 from decimal placement error.

⚠️

Student Fallacy (Why candidates pick this trap): Decimal place arithmetic error.

4 4

✗ Incorrect

Verdict & Scientific Reason:

This is the secondary current ( $I_s = 44\text{ W} / 11\text{ V} = 4\text{ A}$ ), not the primary current.

⚠️

Student Fallacy (Why candidates pick this trap): Calculating secondary current instead of primary current.

⚠️

NTA Trap Alert: Secondary Current vs. Primary Current Trap

Calculating $I = 44 / 11 = 4\text{ A}$ gives the SECONDARY current, which NTA intentionally set as Option (4). The question specifically asks for the current in the PRIMARY circuit, which is $I_p = 44 / 220 = 0.2\text{ A}$ .

🛡️ How to avoid the -1 mark: Check the subscript: Primary current

I_p = P / V_p = 44 / 220 = 0.2\text{ A}

📖

Core NEET Syllabus Standard

NCERT Physics · Alternating Current Standard Benchmark

Core Scientific Principle Tested:

"In an ideal transformer with zero power loss, primary input power equals secondary output power: $V_p I_p = V_s I_s$ ."

Syllabus Focus: Transformers

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Physics Question 50 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Conservation of Power: P_primary = P_secondary

Step-by-Step Rigorous Workflow & Mathematical Proof

Formulating the Ideal Transformer Power Equality

Calculating the Primary Current (I_p)

Verifying via Turns Ratio and Secondary Current

360° Option Elimination Engine Key Feature

NTA Trap Alert: Secondary Current vs. Primary Current Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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