Q.38 Physics ⭐ 360° Option Elimination Active

NEET 2021 Physics Question 38 Solution

Topic: Current Electricity · Official NTA Booklet Code M1

Question

Three resistors having resistances r1, r2 and r3 are connected as shown in the given circuit. The ratio 3 i i of currents in terms of resistances used in the circuit is:

(1)r r r +
(2)r r r +
(3)r r r +
(4)r r r +

✓

Verified Against NTA Final Answer Key

Option (2) : r2 / (r2 + r3)

📚 Current Electricity Easy

📋 Given Parameters & Problem Setup

Total Current entering network i_1

Branch Resistor 2 r_2 (current i_2)

Branch Resistor 3 r_3 (current i_3)

Series Resistor r_1 (carries full current i_1)

⚡

The 30-Second Exam Hall Shortcut: ⚡ Inverse Resistance Current Divider Rule

⏱️ Save ~20 seconds

By Kirchhoff's junction rule, total current entering parallel branches is $i_1 = i_2 + i_3$ . Parallel branches share identical voltage ( $i_2 r_2 = i_3 r_3$ ). The fraction of current flowing through branch 3 is inversely proportional to $r_3$ : $i_3 = i_1 \frac{r_2}{r_2 + r_3} \implies \frac{i_3}{i_1} = \frac{r_2}{r_2 + r_3}$ ! Instant 5-second answer matching Option (2)!

1 Total current

i_1

flows through

r_1

and then splits into branches

r_2

and

r_3

i_1 = i_2 + i_3

2 Since branches

r_2

and

r_3

are in parallel, voltage across them is equal:

V_p = i_2 r_2 = i_3 r_3

3 Substitute

i_2 = i_1 - i_3

(i_1 - i_3) r_2 = i_3 r_3 \implies i_1 r_2 = i_3 (r_2 + r_3)

4 Divide by

i_1

\frac{i_3}{i_1} = \frac{r_2}{r_2 + r_3}

5 Match Option (2).

🛡️

Why You Can 100% Trust This Shortcut: Canonical current division rule for two parallel resistors.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Applying Kirchhoff's Current Law (KCL)

Current $i_1$ enters from terminal A and passes entirely through resistor $r_1$ . At the junction ahead of $r_1$ , the current divides into two parallel branches containing $r_2$ and $r_3$ :

i_1 = i_2 + i_3 \implies i_2 = i_1 - i_3

Step 2

Equating Potential Difference Across Parallel Branches

Because resistors $r_2$ and $r_3$ are connected across the exact same pair of nodes, their potential drops are equal:

V_2 = V_3 \implies i_2 r_2 = i_3 r_3

Step 3

Solving for the Current Ratio i3 / i1

Substitute $i_2 = i_1 - i_3$ into the voltage equality equation:

(i_1 - i_3) r_2 = i_3 r_3 \implies i_1 r_2 - i_3 r_2 = i_3 r_3 \implies i_1 r_2 = i_3 (r_2 + r_3) \implies \frac{i_3}{i_1} = \frac{r_2}{r_2 + r_3}

⭐

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:

Inappropriately includes $r_1$ , which is in series and does not participate in the parallel current division.

⚠️

Student Fallacy (Why candidates pick this trap): Assuming the series resistor determines branch current splitting.

2 2

✓ 100% Correct

Verdict & Scientific Reason:

Exact current divider formula for branch $r_3$ ( $i_3 / i_1 = r_2 / (r_2 + r_3)$ ).

💡

Why this is airtight: None; textbook circuit law.

3 3

✗ Incorrect

Verdict & Scientific Reason:

Omits $r_3$ completely.

⚠️

Student Fallacy (Why candidates pick this trap): Mismatched resistor labels.

4 4

✗ Incorrect

Verdict & Scientific Reason:

Replaces $r_2$ in denominator with series resistance $r_1$ .

⚠️

Student Fallacy (Why candidates pick this trap): Treating

r_1

and

r_3

as the parallel pair.

⚠️

NTA Trap Alert: Opposite Resistor Rule in Current Divider Trap

In a current divider, the current in branch 3 ( $i_3$ ) depends on the OPPOSITE branch resistance $r_2$ in the numerator: $i_3 \propto \frac{r_2}{r_2 + r_3}$ . Students often mistakenly place $r_3$ in the numerator.

🛡️ How to avoid the -1 mark: Higher resistance draws LESS current! Hence

i_3

must have the other resistor (

r_2

) in the numerator.

📖

Core NEET Syllabus Standard

NCERT Physics · Current Electricity Standard Benchmark

Core Scientific Principle Tested:

"In parallel branches, current divides inversely proportional to resistance: $i_3 = i_1 \frac{r_2}{r_2 + r_3}$ ."

Syllabus Focus: Kirchhoff's Rules and Current Division

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Physics Question 38 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Inverse Resistance Current Divider Rule

Step-by-Step Rigorous Workflow & Mathematical Proof

Applying Kirchhoff's Current Law (KCL)

Equating Potential Difference Across Parallel Branches

Solving for the Current Ratio i3 / i1

360° Option Elimination Engine Key Feature

NTA Trap Alert: Opposite Resistor Rule in Current Divider Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Current Electricity

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

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