Question

Which of the following does not represent electric power in the circuit ?

• A. I$^2$R
• B. IR$^2$
• C. VI
• D. $\frac{V^2}{R}$

Hint:

The three common formulas for electric power are $P=VI$, $P=I^2R$, and $P=V^2/R$. These are all derived from the fundamental definition of power and Ohm's Law. Any other combination, like $IR^2$, is generally incorrect.

Answer 1

The Correct Option is B

Step 1: Recall the standard formulas for electric power.
Electric power ($P$) in a circuit can be expressed in several ways, derived from Ohm's Law ($V = IR$). The primary formula is:
$P = VI$ (Power equals Voltage times Current) Step 2: Derive other power formulas using Ohm's Law.
Substitute $V = IR$ into $P = VI$: $P = (IR)I = I^2R$
Substitute $I = V/R$ into $P = VI$: $P = V(\frac{V}{R}) = \frac{V^2}{R}$ Step 3: Evaluate each given option based on the derived formulas.
(1) I$^2$R: This is a correct formula for electric power.
(2) IR$^2$: This is NOT a standard formula for electric power. The current is multiplied by the square of the resistance, which is incorrect.
(3) VI: This is a correct and fundamental formula for electric power.
(4) $\frac{V^2}{R}$: This is a correct formula for electric power. Step 4: Identify the option that does not represent electric power. Based on the analysis, IR$^2$ does not represent electric power. $$(2) IR$^2$$$