How are three resistances $ 3 \, \Omega $, $ 4 \, \Omega $, an... | General Science MCQ | Examoogle

General SciencePrevious Year Paper 2024

How are three resistances $3 \, \Omega$ , $4 \, \Omega$ , and $6 \, \Omega$ connected in combination, so that their total resistance will be $13 \, \Omega$ ?

$3 \, \Omega$ in series with $6 \, \Omega$ and $4 \, \Omega$ in parallel

All in parallel

All in series

Does not depend on any combination

Correct Answer

🔬 SC • Science Concept & PrincipleGeneral SciencePrevious Year Paper 2024

Option C

All in series

Quick Summary:

To obtain a total resistance of $13 \, \Omega$ from $3 \, \Omega$ , $4 \, \Omega$ , and $6 \, \Omega$ resistors, they must all be connected in series. The total resistance in a series circuit is the simple algebraic sum of individual resistances ( $R_{eq} = R_1 + R_2 + R_3$ ).

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🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of resistors in series like adding sections of a pipe with varying widths in a single long path; the total resistance to water flow is the sum of the resistance of each segment.

🧠 Memory Mnemonic / Shortcut Aid

Series Sums: 'In a line, just align and combine.'

🔢 Key Formulas

$R_{eq} = R_1 + R_2 + R_3$ — Series connection formula for equivalent resistance

$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$ — Parallel connection formula for equivalent resistance

⚙️ Working Principle

In a series circuit, current remains constant through all resistors and the total voltage is divided. The equivalent resistance is calculated by $R_{total} = R_1 + R_2 + R_3 +... + R_n$ . Here, $3 \, \Omega + 4 \, \Omega + 6 \, \Omega = 13 \, \Omega$ .

📌 Key Points

▸
Series connection increases the total resistance of the circuit.
▸
Parallel connection decreases the total resistance, making it less than the smallest individual resistance.
▸
The sum $3 + 4 + 6 = 13$ confirms the series configuration.

✅ Advantages

▸
Simple method for increasing resistance values in a circuit.

❌ Disadvantages / Limitations

▸
If one component in a series circuit fails, the entire circuit is broken.

🛠️ Applications / Uses

▸
String lights (older models)
▸
Voltage dividers

📄 Additional Information

▸
Option A (3 in series with 6 and 4 in parallel): $R = 3 + (\frac{6 \times 4}{6 + 4}) = 3 + 2.4 = 5.4 \, \Omega$ .
▸
Option B (All in parallel): $R = \frac{1}{\frac{1}{3} + \frac{1}{4} + \frac{1}{6}} = \frac{1}{\frac{4+3+2}{12}} = \frac{12}{9} \approx 1.33 \, \Omega$ .

📊 Diagram / Illustration

✅

C is correct — Connecting all resistors in series results in their values adding up directly to $3 + 4 + 6 = 13 \, \Omega$ .

Core Concepts Used

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Series circuit Ohm's law Equivalent resistance

💡 EXAM TIP

Always check the 'series' condition ( $R_{eq} = \sum R$ ) before testing more complex parallel calculations in competitive exams.

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