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General SciencePhysics: Electricity

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Calculate the power consumed by a device having a resistance of 40 ohms when connected to a 200 V DC supply.

500 W

1000 W

2000 W

4000 W

Correct Answer

⚙️ TE • Technical Concept & PrincipleGeneral SciencePhysics: Electricity

Option B

1000 W

Quick Summary:

The power consumed by an electrical device is determined by the rate at which electrical energy is converted into other forms, such as heat or light. By applying the formula $P = \frac{V^2}{R}$ , where $V$ is voltage and $R$ is resistance, we calculate the power to be $1000 \text{ W}$ .

🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of electrical power like the water pressure in a pipe; if you keep the same size nozzle (resistance), increasing the pump pressure (voltage) significantly increases the amount of water (energy) passing through per second.

🔢 Key Formulas

$P = \frac{V^2}{R}$ — Power in terms of Voltage and Resistance

$V = IR$ — Ohm's Law

⚙️ Working Principle

The power $P$ in a DC circuit is given by the product of voltage and current ( $P = VI$ ). According to Ohm's Law ( $V = IR$ ), the current can be expressed as $I = \frac{V}{R}$ . Substituting this into the power formula yields $P = V \times (\frac{V}{R}) = \frac{V^2}{R}$ . This shows that for a constant resistance, power increases with the square of the voltage.

📌 Key Points

▸
Electrical power is measured in Watts (W) or Joules per second (J/s).
▸
The power dissipation is directly proportional to the square of the applied voltage.
▸
Higher resistance limits current and reduces power consumption for a fixed voltage.

✅ Advantages

▸
Useful for calculating heating element ratings in appliances like toasters or heaters.

❌ Disadvantages / Limitations

▸
Does not account for inductive reactance in AC circuits, only valid for resistive DC loads.

🛠️ Applications / Uses

▸
Designing filament bulbs and resistive heating elements.
▸
Circuit breaker sizing based on load current calculation.

📄 Additional Information

▸
Calculation: $P = \frac{200^2}{40} = \frac{40000}{40} = 1000 \text{ W}$ .
▸
Option A (500 W) occurs if voltage is incorrectly squared as $200$ instead of $40000$ . Option C and D represent arithmetic errors.

📊 Diagram / Illustration

✅

B is correct — The power consumed is calculated using the relation $P = \frac{V^2}{R}$ , resulting in $1000 \text{ W}$ .

Core Concepts Used

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Electrical Power Ohm's Law Resistive Circuits

💡 EXAM TIP

In competitive exams, always check if the voltage is squared when calculating power for resistive loads to avoid simple calculation errors.

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