Ten resistors having the same value of resistance i.e. 10 ohm,... | General Science MCQ | Examoogle

General SciencePhysics: Electricity

Ten resistors having the same value of resistance i.e. 10 ohm, are connected in parallel. What will be the equivalent resistance of this connection?

2 ohm

5 ohm

100 ohm

1 ohm

Correct Answer

⚙️ TE • Technical Concept & PrincipleGeneral SciencePhysics: Electricity

Option D

1 ohm

Quick Summary:

When $n$ identical resistors each of value $R$ are connected in parallel, the equivalent resistance $R_{eq}$ is given by $\frac{R}{n}$ . With ten $10 \, \Omega$ resistors in parallel, the calculation yields $\frac{10}{10} = 1 \, \Omega$ .

🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of parallel resistors as multiple checkout counters at a supermarket; adding more counters (resistors in parallel) reduces the total waiting time (resistance) for customers (current) to pass through.

🔢 Key Formulas

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

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

⚙️ Working Principle

In a parallel circuit, the reciprocal of the total resistance is equal to the sum of the reciprocals of individual resistances: $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} +... + \frac{1}{R_n}$ . Since all resistors are identical ( $R_1 = R_2 =... = R = 10 \, \Omega$ ), the formula simplifies to $\frac{1}{R_{eq}} = \frac{n}{R}$ , or $R_{eq} = \frac{R}{n}$ . This configuration provides multiple paths for current to flow, thereby reducing the total effective resistance.

📌 Key Points

▸
Equivalent resistance in parallel is always less than the smallest individual resistance in the group.
▸
Connecting identical resistors in parallel reduces the overall resistance proportionally to the number of resistors.
▸
Voltage remains the same across all components in a parallel connection.

✅ Advantages

▸
Failure of one resistor does not stop the current flow through others.
▸
Allows for lower total resistance using components of higher resistance values.

❌ Disadvantages / Limitations

▸
Requires more wiring compared to series connections.
▸
The total current drawn from the source increases significantly as more resistors are added in parallel.

🛠️ Applications / Uses

▸
Household electrical wiring (all appliances in parallel).
▸
Voltage distribution circuits.

📄 Additional Information

▸
Option A ( $2 \, \Omega$ ) is incorrect, it would result from five $10 \, \Omega$ resistors.
▸
Option B ( $5 \, \Omega$ ) is incorrect, it would result from two $10 \, \Omega$ resistors.
▸
Option C ( $100 \, \Omega$ ) is incorrect, it would result from connecting ten $10 \, \Omega$ resistors in series ( $R_{eq} = n \times R$ ).

📊 Diagram / Illustration

✅

D is correct — The equivalent resistance of $n$ identical resistors in parallel is calculated by dividing the individual resistance by the number of resistors, resulting in $1 \, \Omega$ .

Core Concepts Used

Click any tag to open in AI Tutor

Parallel Circuit Ohm's Law Equivalent Resistance

💡 EXAM TIP

Always remember: Adding resistors in parallel decreases the net resistance, while adding them in series increases the net resistance.

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)