In direct-current (DC) circuit analysis, different forms of Watt's Law are used depending … — Armed Services Vocational Aptitude Battery (ASVAB)

In direct-current (DC) circuit analysis, different forms of Watt's Law are used depending on which electrical quantities are known. Match each set of known circuit parameters on the left with the correct formula on the right used to calculate the target value directly.

Known voltage ( $V$ ) and current ( $I$ ) to calculate total power ( $P$ ) $P = V \times I$
Known current ( $I$ ) and resistance ( $R$ ) to calculate power dissipation ( $P$ ) $P = I^2 \times R$
Known voltage ( $V$ ) and resistance ( $R$ ) to calculate power dissipation ( $P$ ) $P = \frac{V^2}{R}$
Known power rating ( $P$ ) and operating voltage ( $V$ ) to calculate operating current ( $I$ ) $I = \frac{P}{V}$

Answer

Each given set of circuit parameters matches the direct algebraic form of Watt's Law designed for those specific variables: Voltage and Current to

P = V \times I

; Current and Resistance to

P = I^2 \times R

; Voltage and Resistance to

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

; and Power and Voltage to

I = \frac{P}{V}

Each match correctly pairs the given known variables with the exact Watt's Law equation variant required to solve directly for the unknown quantity without needing extraneous calculation steps.

Step-by-Step Solution

Identify the base definition of electrical power in terms of voltage and current.

P = V \times I

Power in watts equals electromotive force in volts multiplied by electron current flow in amperes.

Derive the power formula when only current and resistance are given using Ohm's Law (

V = I \times R

P = (I \times R) \times I = I^2 \times R

Replacing voltage with the product of current and resistance calculates power without needing voltage explicitly.

Derive the power formula when only voltage and resistance are given using Ohm's Law (

I = \frac{V}{R}

P = V \times \left(\frac{V}{R}\right) = \frac{V^2}{R}

Replacing current with voltage divided by resistance calculates power without needing current explicitly.

Rearrange the primary power formula to solve for current when power and voltage are known.

I = \frac{P}{V}

Dividing both sides of

P = V \times I

by voltage isolates the current parameter.

Key Concept

Watt's Law and its derived variations relate electrical power (

P

), voltage (

V

), current (

I

), and resistance (

R

Estimated Time:45s

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