What is the relation between Power (P), Voltage (V), and Resistance (R)?

Appeared in: DSSSB - 28 August 2019 (Shift-1)

Explanation

The correct formula is P = V²/R, which states that power is directly proportional to the square of the voltage and inversely proportional to the resistance.
This relationship is derived by combining the basic power formula (P = V × I) with Ohm's Law (I = V / R).
By substituting 'V/R' for 'I' in the power equation, we get P = V × (V/R), which simplifies to P = V²/R.

Option A: This formula (P = VR²) does not represent a standard physical relationship for calculating electrical power.
Option B: The formula P = V/R is incorrect for power. The expression V/R is used to calculate Current (I) according to Ohm's Law (I = V/R).
Option C: This formula (P = V/R²) is mathematically incorrect for calculating electrical power.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Relationship between Electrical Power, Voltage, and Resistance as background academic context rather than a clinical decision trigger.
Understanding the relationship between voltage, resistance, and power is critical for ensuring electrical safety in clinical settings, especially when using high-power devices like defibrillators or electrosurgical units.
Nurses must be aware that lower skin resistance (e.g., due to moisture) can lead to more severe burns or shocks for a given voltage, as power (and thus heat) is inversely proportional to resistance (P = V²/R).
What if? If a device has a fixed voltage but its resistance is halved (e.g., due to a short circuit or wet contact), the power dissipated will double (P = V²/R). This dramatically increases the risk of overheating, fire, or patient injury.

How to Approach the Question

First, identify the core concepts in the question: Power (P), Voltage (V), and Resistance (R).
Recall the two fundamental laws of basic electricity: the power law (P = V × I) and Ohm's law (V = I × R).
Recognize that the question asks for a formula with P, V, and R, which means the 'I' (Current) term must be eliminated.
Rearrange Ohm's Law to solve for I (I = V / R).
Substitute this expression for I into the power law: P = V × (V / R).
Simplify the expression to arrive at the final formula: P = V² / R, and select the matching option.

Concept Tested & Keywords

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Practise the full DSSSB - 28 August 2019 (Shift-1)

Attempt every question from this paper in a timed mock, then review the full solution for each one.