If four resistors, each having a resistance of $12 \Omega$, ar... | General Science MCQ | Examoogle

General SciencePhysics: Electricity

If four resistors, each having a resistance of $12 \Omega$ , are connected in parallel, what will be the effective resistance of the circuit?

3 , $\Omega$

4 , $\Omega$

6 , $\Omega$

48 , $\Omega$

Correct Answer

⚙️ TE • Technical Concept & PrincipleGeneral SciencePhysics: Electricity

Option A

3 , $\Omega$

Quick Summary:

When resistors are connected in parallel, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances. For $n$ identical resistors each of resistance $R$ connected in parallel, the equivalent resistance $R_{eq}$ is given by $\frac{R}{n}$ .

🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of parallel resistors as adding more checkout lanes at a grocery store; the more lanes you open, the easier it is for customers to pass through, reducing the overall bottleneck (resistance).

🔢 Key Formulas

$\frac{1}{R_{eq}} = \sum_{i=1}^{n} \frac{1}{R_i}$ — General formula for parallel resistors

$R_{eq} = \frac{R}{n}$ — Simplified formula for $n$ identical resistors in parallel

⚙️ Working Principle

In a parallel circuit, the voltage across each resistor remains the same, but the total current is divided among the branches. Adding more resistors in parallel provides additional paths for the current to flow, thereby reducing the total effective resistance of the circuit. Mathematically, $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} +... + \frac{1}{R_n}$ .

📌 Key Points

▸
The equivalent resistance in a parallel circuit is always smaller than the smallest individual resistor.
▸
If $n$ resistors of equal resistance $R$ are connected in parallel, the effective resistance is $R/n$ .
▸
Adding more resistors in parallel decreases the total circuit resistance.

✅ Advantages

▸
If one component fails, the others continue to function independently.

❌ Disadvantages / Limitations

▸
Requires more wiring compared to series circuits.

🛠️ Applications / Uses

▸
Domestic wiring (all appliances operate at the same voltage).
▸
Lighting circuits in buildings.

📄 Additional Information

▸
Given $R = 12 \,\Omega$ and $n = 4$ , $R_{eq} = \frac{12}{4} = 3 \,\Omega$ .
▸
Option B (4 , $\Omega)$ is incorrect as it results from misapplying the reciprocal rule.
▸
Option C (6 , $\Omega)$ is incorrect as it results from incorrectly dividing by 2 instead of 4.
▸
Option D (48 , $\Omega)$ is incorrect as it represents the total resistance of resistors connected in series ( $n \times R$ ).

📊 Diagram / Illustration

✅

A is correct — The effective resistance is calculated as $\frac{12 \,\Omega}{4} = 3 \,\Omega$ .

Core Concepts Used

Click any tag to open in AI Tutor

Ohm's Law Parallel Circuit Equivalent Resistance

💡 EXAM TIP

Always remember: Adding resistors in series increases total resistance ( $R_{total} = R_1 + R_2 +...$ ), while adding resistors in parallel decreases it.

Was this solution helpful?

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Related Questions

Discussion (0)