Match each Watt's Law power formula or electrical power unit on the left with its correspo… — Armed Services Vocational Aptitude Battery (ASVAB)

Match each Watt's Law power formula or electrical power unit on the left with its corresponding definition or application condition on the right.

$P = V \times I$ Calculates electrical power directly when voltage and current are known
$P = I^2 R$ Calculates electrical power directly when current and resistance are known
$P = \frac{V^2}{R}$ Calculates electrical power directly when voltage and resistance are known
$1\text{ Watt (W)}$ The standard unit of electrical power, equivalent to one joule per second ( $1\text{ J/s}$ )

Answer

P = V \times I

matches power from voltage and current;

P = I^2 R

matches power from current and resistance;

P = \frac{V^2}{R}

matches power from voltage and resistance;

1\text{ Watt (W)}

matches the unit equivalent to one joule per second.

Each formula represents a direct algebraic variation of Watt's Law derived by combining

P = V \times I

with Ohm's Law (

V = IR

), and the watt is defined as one joule per second.

Step-by-Step Solution

Identify the base relationship of Watt's Law

P = V \times I

Electrical power is defined as the rate at which electrical energy is transferred, calculated by multiplying voltage across a load by the current flowing through it.

Derive the formula relating power to current and resistance

P = I^2 R

By substituting

V = I \times R

from Ohm's Law into

P = V \times I

, power is expressed in terms of current squared times resistance.

Derive the formula relating power to voltage and resistance

P = \frac{V^2}{R}

By substituting

I = \frac{V}{R}

from Ohm's Law into

P = V \times I

, power is expressed in terms of voltage squared divided by resistance.

Identify the standard unit and definition of power

1\text{ W} = 1\text{ J/s}

Power measures the rate of doing work or dissipating energy, where one watt equals one joule per second.

Key Concept

Watt's Law and Electrical Power Formulas

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