Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option D

$P = VI$

Quick Summary: In an electrical circuit, the instantaneous power $P$ dissipated in a pure resistor is defined as the product of the voltage across the component $V$ and the current flowing through it $I$. This relationship is derived from the principle of conservation of energy where power is the rate at which electrical energy is converted into thermal energy.

💡 Explanation

In an electrical circuit, the instantaneous power $P$ dissipated in a pure resistor is defined as the product of the voltage across the component $V$ and the current flowing through it $I$ . This relationship is derived from the principle of conservation of energy where power is the rate at which electrical energy is converted into thermal energy.

🔢 Key Formulas

$P = VI$ — Power in terms of Voltage and Current

$P = I^2R$ — Power in terms of Current and Resistance

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

⚙️ Working Principle

According to Joule's Law of heating, when a current $I$ flows through a resistor $R$ across a potential difference $V$ , the work done per unit time is given by the product of charge flow rate (current) and potential energy difference. Since $V = IR$ (Ohm's Law), the power can also be expressed as $P = I^2R$ or $P = V^2/R$ . In a purely resistive circuit, the phase angle is zero, making the power factor unity.

📌 Key Points

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Power in a purely resistive circuit is always positive, representing energy dissipation as heat.
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The power factor for a pure resistor is always 1 (unity).
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Instantaneous power is the rate of energy consumption at a specific moment in time.
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For AC circuits, $P = VI \cos \phi$ , where $\cos \phi = 1$ for a resistor.

✅ Advantages

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Simple linear relationship between variables.
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Calculations are independent of frequency.

❌ Disadvantages / Limitations

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Does not account for reactive components like inductors or capacitors in practical loads.
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Does not consider phase shifts present in non-resistive circuits.

🛠️ Applications / Uses

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Electric heating elements (heaters, toasters).
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Incandescent lighting systems.
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Calibration of resistive loads in testing.

📄 Additional Information

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Units: Power is measured in Watts ( $W$ ), Voltage in Volts ( $V$ ), and Current in Amperes ( $A$ ).
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Option A ( $P=V/I$ ) represents Resistance $R$ . Option B ( $P=I/V$ ) represents Conductance $G$ . Option C ( $P=IR$ ) has no physical meaning as a power unit.

📊 Diagram / Illustration

✅

D is correct — The power consumed by a pure resistor is directly given by the product of the potential difference and the current flowing through it, expressed as $P=VI$ .

Core Concepts Used

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Joule's Law Ohm's Law Electrical Power

💡 EXAM TIP

Remember that $P=VI$ is valid for any DC circuit or instantaneous AC value; use $P=VI\cos \phi$ when calculating real power in general AC circuits.

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