Q.37 Physics · Section B ⭐ 360° Option Elimination Active

NEET 2024 Physics Question 37 Solution

Topic: Current Electricity · Official NTA Booklet Code T1

Question

Two heaters A and B have power rating of 1 kW and 2 kW, respectively. Those two are first connected in series and then in parallel to a fixed power source. The ratio of power outputs for these two cases is:

✓

Verified Against NTA Final Answer Key

Option (4) : 2 : 9

📚 Current Electricity Easy

📋 Given Parameters & Problem Setup

Heater A power rating P_A = 1 kW

Heater B power rating P_B = 2 kW

Source voltage Same fixed power source V

⚡

The 30-Second Exam Hall Shortcut: ⚡ Power Reciprocal Product Rule

⏱️ Save ~45 seconds

Series power: 1/P_s = 1/1 + 1/2 = 3/2 -> P_s = 2/3 kW. Parallel power: P_p = 1 + 2 = 3 kW. Ratio P_s / P_p = (2/3) / 3 = 2 : 9!

1 In series across fixed voltage V: 1 / P_series = 1 / P_A + 1 / P_B = 1 / 1 + 1 / 2 = 3/2 => P_series = 2/3 kW.

2 In parallel across fixed voltage V: P_parallel = P_A + P_B = 1 + 2 = 3 kW.

3 Ratio of power outputs: P_series / P_parallel = (2/3) / 3 = 2 / 9 = 2 : 9.

4 Option (4) in 10 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Power Dissipation Formula for Fixed Voltage Source (P_parallel = Σ P_i, 1/P_series = Σ 1/P_i).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Resistances of Heaters from Rated Power

For a heater designed for rated voltage V, power is P = V² / R, which gives resistance R = V² / P:

R_A = \frac{V^2}{P_A} = \frac{V^2}{1\,\text{kW}}, \quad R_B = \frac{V^2}{P_B} = \frac{V^2}{2\,\text{kW}} = \frac{R_A}{2}

Step 2

Case 1: Heaters in Series

When connected in series across the same fixed voltage source V, the total equivalent resistance is:

R_{series} = R_A + R_B = R_A + \frac{R_A}{2} = \frac{3}{2} R_A

Step 3

Power Output in Series

The power delivered in the series configuration is:

P_{series} = \frac{V^2}{R_{series}} = \frac{V^2}{\frac{3}{2} R_A} = \frac{2}{3} \frac{V^2}{R_A} = \frac{2}{3} P_A = \frac{2}{3}\,\text{kW}

Step 4

Case 2: Heaters in Parallel

When connected in parallel across the same fixed voltage V, each heater has the full source voltage across it. Power outputs add directly:

P_{parallel} = P_A + P_B = 1\,\text{kW} + 2\,\text{kW} = 3\,\text{kW}

Step 5

Ratio of Power Outputs

Taking the ratio of the series power to parallel power:

\frac{P_{series}}{P_{parallel}} = \frac{2/3\,\text{kW}}{3\,\text{kW}} = \frac{2}{9} \implies P_{series} : P_{parallel} = 2 : 9

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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:

This is the ratio of the individual heater powers (1 kW : 2 kW).

⚠️

Student Fallacy (Why candidates pick this trap): Confusing individual power ratings with series-to-parallel combination ratio.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Represents only P_series in kW, forgetting to divide by P_parallel = 3 kW.

⚠️

Student Fallacy (Why candidates pick this trap): Stopping at P_series = 2/3.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Physical impossibility; parallel power is always much greater than series power.

⚠️

Student Fallacy (Why candidates pick this trap): Assuming power is conserved regardless of circuit configuration.

4 (4)

✓ 100% Correct

Verdict & Scientific Reason:

Exact ratio: (2/3) / 3 = 2/9.

💡

Why this is airtight: None.

⚠️

NTA Trap Alert: Power Formulas Inversion Trap

Students frequently remember "P = I²R so series adds", forgetting that current I is drastically reduced in series when connected to a fixed VOLTAGE source.

🛡️ How to avoid the -1 mark: For fixed voltage V: In parallel, powers add directly (P_p = P1 + P2); in series, reciprocal powers add (1/P_s = 1/P1 + 1/P2)!

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Core NEET Syllabus Standard

Physics Core Electrodynamics · Current Electricity Standard Benchmark

Core Scientific Principle Tested:

"Across a constant voltage source, P_parallel = P1 + P2 and 1/P_series = 1/P1 + 1/P2."

Syllabus Focus: Electric Power and Heating Effects of Current

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Series adds reciprocals (2/3); Parallel adds direct (3) -> Ratio is 2 to 9!

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NEET 2024 Physics Question 37 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Power Reciprocal Product Rule

Step-by-Step Rigorous Workflow & Mathematical Proof

Resistances of Heaters from Rated Power

Case 1: Heaters in Series

Power Output in Series

Case 2: Heaters in Parallel

Ratio of Power Outputs

360° Option Elimination Engine Key Feature

NTA Trap Alert: Power Formulas Inversion Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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Current Variation with Temperature for Series and Parallel Dual-Coefficient Resistors

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