Which of the following formulas is NOT a correct representatio... | General Science MCQ | Examoogle

Back to Practice Questions

General SciencePhysics: Electricity

Prev Next

Which of the following formulas is NOT a correct representation for electric power (P) in a circuit?

P = VI

P = I² R

P = V² / R

P = IR²

Correct Answer

⚙️ TE • Technical Concept & PrincipleGeneral SciencePhysics: Electricity

Option D

P = IR²

Quick Summary:

Electric power is defined as the rate at which electrical energy is transferred or converted into other forms of energy in an electric circuit. The formulas $P = VI$ , $P = I^2R$ , and $P = \frac{V^2}{R}$ are all valid representations derived from Ohm's Law, whereas $P = IR^2$ is dimensionally incorrect.

🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of power as the 'rate of doing work' in a pipeline; $P = VI$ is like multiplying the water pressure by the flow rate, while $P = IR^2$ tries to multiply the flow rate by the pipe's resistance squared, which holds no physical meaning for the total output.

🧠 Memory Mnemonic / Shortcut Aid

P = VI (VI) → P = I² R (I squared R) → P = V² / R (V squared over R)

🔢 Key Formulas

$P = VI$ — Basic definition of power

$P = I^2R$ — Power in terms of current and resistance

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

⚙️ Working Principle

According to Ohm's Law, $V = IR$ . Substituting this into the primary power formula $P = VI$ yields $P = (IR) \times I = I^2R$ . Alternatively, substituting $I = \frac{V}{R}$ into $P = VI$ yields $P = V \times (\frac{V}{R}) = \frac{V^2}{R}$ . Since the formula $P = IR^2$ does not satisfy the algebraic substitution of Ohm's Law, it does not represent physical power.

📌 Key Points

▸
The SI unit of electric power is the Watt ( $W$ ), where $1 W = 1 J/s$ .
▸
Electric power represents the rate of energy dissipation as heat in a resistor.
▸
Ohm's Law is the foundation for deriving all variations of the power formula.

✅ Advantages

▸
Using $P = I^2R$ is convenient when components are connected in series (same current).
▸
Using $P = \frac{V^2}{R}$ is convenient when components are connected in parallel (same voltage).

🛠️ Applications / Uses

▸
Calculating the wattage rating of household appliances.
▸
Designing electrical circuits to prevent overheating of components.

📄 Additional Information

▸
Option D is incorrect because it relates current and resistance with an incorrect exponent, violating the unit analysis where power must have dimensions of $[ML^2T^{-3}]$ .
▸
Power is a scalar quantity.

📊 Diagram / Illustration

✅

D is correct — The formula $P = IR^2$ is not a valid representation of electric power as it is dimensionally inconsistent with the physical definition of power.

Core Concepts Used

Click any tag to open in AI Tutor

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

💡 EXAM TIP

When solving electricity problems, always check if components are in series ( $I$ constant) or parallel ( $V$ constant) to choose the most efficient power formula.

Was this solution helpful?

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Related Questions

Discussion (0)