A resistor whose value $ R = 10 \ \Omega $ is connected to a 1... | General Science MCQ | Examoogle

General SciencePrevious Year Paper 2024

A resistor whose value $R = 10 \ \Omega$ is connected to a 10-volt battery. What will be the power $P$ and the amount of heat $H$ generated in one minute?

$P = 100 \text{ W}, H = 6000 \text{ J}$

$P = 1 \text{ W}, H = 60 \text{ J}$

$P = 20 \text{ W}, H = 1200 \text{ J}$

$P = 10 \text{ W}, H = 600 \text{ J}$

Correct Answer

🔬 SC • Science Concept & PrincipleGeneral SciencePrevious Year Paper 2024

Option D

$P = 10 \text{ W}, H = 600 \text{ J}$

Quick Summary:

To find the power and heat, we use the basic formulas for electrical power and energy. Power ( $P$ ) is the rate of energy dissipation, calculated as $P = \frac{V^2}{R}$ . Heat ( $H$ ) is the total energy dissipated over time ( $t$ ), calculated as $H = P \times t$ .

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🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of a light bulb: a 10-watt bulb consumes energy at a rate of 10 joules every second. If you keep it on for a minute, it will have used 600 joules of electrical energy to produce light and heat.

🔢 Key Formulas

$P = \frac{V^2}{R}$ — Formula for Power dissipated in a resistor

$H = P \times t$ — Formula for Heat generated over time

⚙️ Working Principle

When a voltage ( $V$ ) is applied across a resistor ( $R$ ), a current ( $I = \frac{V}{R}$ ) flows through it. The resistor dissipates this electrical energy as heat according to Joule's Law. With $V = 10 V$ and $R = 10\,\Omega$ , the power is $P = \frac{10^2}{10} = 10 W$ . Over one minute ( $t = 60 s$ ), the total heat generated is $H = 10 W \times 60 s = 600 J$ .

📌 Key Points

▸
Voltage $V = 10 V$ and Resistance $R = 10\,\Omega$
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Time $t = 1\,\text{minute} = 60\,\text{seconds}$
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Power unit is Watt (W) and Heat/Energy unit is Joule (J)

🛠️ Applications / Uses

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Electrical heating appliances like toasters and heaters
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Calculating efficiency and energy consumption of circuits

📄 Additional Information

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The SI unit of power is the Watt ( $1 W = 1 J/s$ ).
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Option A is incorrect as $100 W$ exceeds the calculated power.
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Option B is incorrect as $1 W$ is too low.
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Option C is incorrect as the values do not match the calculation ( $P=10 W, H=600 J$ ).

📊 Diagram / Illustration

✅

D is correct — The power dissipated is $10 W$ and the heat generated in 60 seconds is $600 J$ .

Core Concepts Used

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Joule's Law of Heating Electrical Power Ohm's Law

💡 EXAM TIP

Always convert time into standard SI units (seconds) before calculating energy/heat in Joules.

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