A 20 ohm resistor is connected to a DC source. Adding another ... | General Science MCQ | Examoogle

General SciencePhysics: Electricity

A 20 ohm resistor is connected to a DC source. Adding another resistor in series causes the current to drop to one-third of the original value. The value of the second resistor is:

20 ohm

40 ohm

60 ohm

10 ohm

Correct Answer

⚙️ TE • Technical Concept & PrincipleGeneral SciencePhysics: Electricity

Option B

40 ohm

Quick Summary:

According to Ohm's law, current is inversely proportional to the total resistance of the circuit when voltage remains constant. Since the current decreases to one-third of its initial value, the total resistance must increase by a factor of three.

🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of current as water flowing through a pipe; adding a second resistor in series is like adding a second narrow section of pipe, which restricts the total flow to one-third of the original speed.

🧠 Memory Mnemonic / Shortcut Aid

VIR: $V = I \times R$ (Voltage equals current times resistance)

🔢 Key Formulas

$V = I \times R$ — Ohm's Law

$R_{\text{total}} = R_1 + R_2$ — Series resistance addition

⚙️ Working Principle

In a series circuit, the total resistance ( $R_{\text{total}}$ ) is the sum of individual resistors ( $R_1 + R_2$ ). Since the voltage ( $V$ ) is constant, the relation $I = \frac{V}{R}$ implies that $I_1 R_1 = I_2 R_2$ . Given $I_2 = \frac{1}{3} I_1$ , we deduce $R_2 = 3 R_1$ . With $R_1 = 20 \,\Omega$ , the total resistance becomes $60 \,\Omega$ , making the added resistor $R_2 = 60 - 20 = 40 \,\Omega$ .

📌 Key Points

▸
Current in a series circuit is the same through all components.
▸
Total resistance in series is always greater than any individual resistor.
▸
If the current becomes $\frac{1}{n}$ of the original value, the total resistance becomes $n$ times the original value.

✅ Advantages

▸
Series circuits allow for simple control of current using a single switch.

❌ Disadvantages / Limitations

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

🛠️ Applications / Uses

▸
Decorative string lights
▸
Current limiting in electronic circuits

📄 Additional Information

▸
Original current $I_1 = \frac{V}{20}$ .
▸
New current $I_2 = \frac{V}{20 + R_2}$ .
▸
Setting $I_2 = \frac{1}{3} I_1$ leads to $20 + R_2 = 60$ , so $R_2 = 40 \,\Omega$ .

📊 Diagram / Illustration

✅

B is correct — Adding a $40 \,\Omega$ resistor in series with a $20 \,\Omega$ resistor triples the total resistance, thereby reducing the current to one-third of its original value.

Core Concepts Used

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Ohm's Law Series Circuit Equivalent Resistance

💡 EXAM TIP

Always check if the voltage is constant. If it is, the inverse proportionality between current and resistance is the fastest way to solve electricity problems.

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