In electrical circuits, the power consumed or dissipated can be calculated using different… — Armed Services Vocational Aptitude Battery (ASVAB)

In electrical circuits, the power consumed or dissipated can be calculated using different formulas depending on which circuit parameters are known. Match each set of known circuit parameters on the left with the correct electrical power formula on the right. How should each parameter combination be paired with its corresponding power formula?

Known Voltage ( $V$ ) and Current ( $I$ ) $P = V \times I$
Known Current ( $I$ ) and Resistance ( $R$ ) $P = I^2 R$
Known Voltage ( $V$ ) and Resistance ( $R$ ) $P = \frac{V^2}{R}$
Known Electrical Energy ( $E$ ) and Time ( $t$ ) $P = \frac{E}{t}$

Answer

Voltage and Current pairs with

P = V \times I

; Current and Resistance pairs with

P = I^2 R

; Voltage and Resistance pairs with

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

; Electrical Energy and Time pairs with

P = \frac{E}{t}

Each parameter combination matches its standard mathematical expression: Voltage and Current relate directly through Watt's Law (

P = V \times I

), Current and Resistance relate through

P = I^2 R

, Voltage and Resistance relate through

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

, and Energy and Time match the foundational definition of power (

P = \frac{E}{t}

Step-by-Step Solution

Identify the base relationship of electrical power from fundamental physical definitions

Power is defined as energy divided by time:

P = \frac{E}{t}

This establishes the core definition of power in Joules per second (Watts).

Identify Watt's Law for circuits when potential difference and flow rate are known

Power is given by

P = V \times I

Multiplying potential difference (Volts) by current (Amperes) yields electrical power in Watts.

Use Ohm's Law substitutions to find power formulas for resistive circuits

When current and resistance are known:

P = I^2 R

. When voltage and resistance are known:

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

Substituting

V = IR

I = \frac{V}{R}

allows power to be determined when one electrical variable is omitted.

Key Concept

Electrical Power and Watt's Law Formulations

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