Consider a parallel combination of 2 resistors with resistance... | General Science MCQ

General SciencePrevious Year Paper 2024

Consider a parallel combination of 2 resistors with resistances $4\,\Omega$ and $6\,\Omega$ . The equivalent resistance of the circuit is:

$12\,\Omega$

$10\,\Omega$

$4.2\,\Omega$

$2.4\,\Omega$

Correct Answer

🔬 SC • Science Concept & PrincipleGeneral SciencePrevious Year Paper 2024

Option D

$2.4\,\Omega$

Quick Summary:

The equivalent resistance ( $R_{eq}$ ) of two resistors connected in parallel is calculated using the formula $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$ . Substituting the given values $R_1 = 4 \ \Omega$ and $R_2 = 6 \ \Omega$ , we get $R_{eq} = \frac{4 \times 6}{4 + 6} = \frac{24}{10} = 2.4 \ \Omega$ .

🎯

Crack Previous Year Paper 2024 with Examoogle SuperTeachers

Get Free Demo Classes & Live Mocks →

🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of parallel resistors as multiple open checkout counters at a supermarket. Having more counters open allows shoppers to flow through more easily, reducing the overall bottleneck (resistance) compared to having only a single counter open.

🧠 Memory Mnemonic / Shortcut Aid

Parallel resistance product over sum: $R_{eq} = \frac{R_1 R_2}{R_1 + R_2}$ .

🔢 Key Formulas

$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$ — Reciprocal formula for two resistors in parallel

$R_{eq} = \frac{R_1 \times R_2}{R_1 + R_2}$ — Simplified product-over-sum formula for two parallel resistors

⚙️ Working Principle

When resistors are connected in parallel, the potential difference across each resistor is the same, but the total current is divided among the parallel branches. This arrangement provides multiple paths for current to flow, which decreases the overall resistance of the circuit compared to any individual resistor in the combination.

📌 Key Points

▸
In a parallel circuit, the equivalent resistance is always smaller than the smallest individual resistance in the combination.
▸
The potential difference (voltage) across each parallel branch remains the same.
▸
The total current entering the parallel combination equals the sum of currents flowing through each individual branch.

✅ Advantages

▸
If one component/appliance fails in a parallel circuit, other components continue to work normally.
▸
Each appliance receives the full source voltage.

❌ Disadvantages / Limitations

▸
Draws higher total current from the source as more branches are added, which can lead to overloading.

🛠️ Applications / Uses

▸
Household electrical wiring (all appliances are connected in parallel)
▸
Distribution networks in electronic printed circuit boards (PCBs)

📄 Additional Information

▸
Option A ( $12 \ \Omega$ ) represents the sum if they were incorrectly added as $4 + 8$ or confusion with series.
▸
Option B ( $10 \ \Omega$ ) represents the series combination resistance ( $4 + 6 = 10 \ \Omega$ ).
▸
Option D ( $2.4 \ \Omega$ ) is the correct calculated parallel equivalent resistance.

📊 Diagram / Illustration

✅

D is correct — The equivalent resistance of a $4 \ \Omega$ and $6 \ \Omega$ resistor in parallel is $

Was this solution helpful?

⚡ Practice on Android App · 4.8 ★

Solve 10,000+ More Questions with AI Tutor

Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.

Free Download • 100K+ Aspirants

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)