Which of the following is not an expression of power?

Question

Examoogle · Accepted Answer

$P = \frac{I}{R}$

Explanation: Power in a DC circuit is defined as the rate at which electrical energy is transferred or converted. The standard expressions derived from Ohm's Law ($V=IR$) are $P=VI$, $P=I^2R$, and $P=\frac{V^2}{R}$, whereas $P=\frac{I}{R}$ is dimensionally inconsistent with the unit of power (Watts).

Working Principle: The electrical power $P$ absorbed by a resistive component is the product of voltage across it and current through it. By substituting $V=IR$ or $I=\frac{V}{R}$ into the fundamental equation $P=VI$, we derive the alternative forms $I^2R$ and $\frac{V^2}{R}$. The expression $\frac{I}{R}$ represents current density or related metrics in different contexts but never electrical power.

Key Formulas: $P = VI$ — Basic electrical power definition; $P = I^2R$ — Power in terms of current and resistance; $P = \frac{V^2}{R}$ — Power in terms of voltage and resistance

Key Points: Electrical power is measured in Watts (W) or Joules per second (J/s).; Ohm's Law ($V=IR$) is the basis for interchanging these power formulas.; The expression $\frac{I}{R}$ does not have the units of power ($Volt 	imes Ampere$).

Advantages: Allows flexibility in calculations based on known parameters (V, I, or R).; Simplifies analysis in series vs. parallel circuit configurations.

Applications: Determining heat dissipation in resistors.; Calculating power ratings for electrical appliances.; Circuit sizing and fuse selection.

Additional Info: Units of $P$ are Watts, $V$ are Volts, $I$ are Amperes, and $R$ are Ohms.. Dimension check: $VI = [V][A] = [Watt]$, $I^2R = [A^2][\Omega] = [A^2][V/A] = [VA] = [Watt]$, $\frac{V^2}{R} = [V^2]/[\Omega] = [V^2]/[V/A] = [VA] = [Watt]$.. Option D is dimensionally $A/\Omega = A^2/V$, which is not equivalent to Power.

Answer: D is correct — The expression $P = I/R$ is dimensionally incorrect and does not represent electrical power.

Exam Tip: Always verify units using dimensional analysis ($W = V 	imes A$) if you are unsure about a specific power formula during an exam.

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