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General SciencePhysics: Electricity

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Calculate the equivalent resistance of three 30 ohm resistors connected in parallel.

90 ohms

10 ohms

30 ohms

3 ohms

Correct Answer

⚙️ TE • Technical Concept & PrincipleGeneral SciencePhysics: Electricity

Option B

10 ohms

Quick Summary:

When resistors are connected in parallel, the reciprocal of the equivalent resistance is the sum of the reciprocals of individual resistances. For three $30 \, \Omega$ resistors, the equivalent resistance is $10 \, \Omega$ .

🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of parallel resistors as adding more lanes to a highway; even if each lane has the same friction (resistance), adding more lanes increases the total traffic capacity, effectively decreasing the overall resistance to flow.

🔢 Key Formulas

$\frac{1}{R_{eq}} = \sum \frac{1}{R_i}$ — General formula for parallel resistors

$R_{eq} = \frac{R}{n}$ — Shortcut for $n$ equal resistors in parallel

⚙️ Working Principle

In a parallel circuit, the voltage across each resistor remains constant, while the total current splits among the branches. According to Ohm's Law and Kirchhoff's Current Law, the total resistance $R_{eq}$ is defined by $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$ . Since all resistors are equal, the formula simplifies to $R_{eq} = \frac{R}{n}$ , where $n$ is the number of resistors.

📌 Key Points

▸
The equivalent resistance in parallel is always less than the smallest individual resistance in the circuit.
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Connecting resistors in parallel decreases the total resistance, whereas connecting in series increases it.

✅ Advantages

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Fault tolerance: If one branch fails, the others continue to function.
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Independent control: Each branch can be switched on or off independently.

❌ Disadvantages / Limitations

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High current drain: Total resistance decreases, potentially leading to excessive current if not managed by fuses or circuit breakers.

🛠️ Applications / Uses

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Domestic electrical wiring for lights and appliances.
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Circuit design requiring low resistance paths.

📄 Additional Information

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Calculation: $\frac{1}{R_{eq}} = \frac{1}{30} + \frac{1}{30} + \frac{1}{30} = \frac{3}{30} = \frac{1}{10}$ . Thus, $R_{eq} = 10 \, \Omega$ .
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Option A ( $90 \, \Omega$ ) is the result if the resistors were connected in series ( $30+30+30$ ).

📊 Diagram / Illustration

✅

B is correct — The equivalent resistance of three identical resistors in parallel is one-third of the value of a single resistor.

Core Concepts Used

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Parallel Circuits Equivalent Resistance Ohm's Law

💡 EXAM TIP

Always identify whether resistors are in series or parallel before applying formulas; in series, add resistances directly, while in parallel, add their reciprocals.

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