A portable communications transceiver connected to a 12\text{ V} direct-current (DC) power… — Armed Services Vocational Aptitude Battery (ASVAB)

A portable communications transceiver connected to a $12\text{ V}$ direct-current (DC) power source consumes $36\text{ W}$ of electrical power during operation. What is the effective resistance of the transceiver circuit?

A
$3\text{ }\Omega$
$4\text{ }\Omega$ Answer
C
$0.33\text{ }\Omega$
D
$432\text{ }\Omega$

Answer

The effective resistance of the transceiver circuit is

4\text{ }\Omega

Electrical power is related to voltage and resistance by the formula

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

. Rearranging this equation to solve for resistance gives

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

. Substituting the given values:

R = \frac{(12)^2}{36} = \frac{144}{36} = 4\text{ }\Omega

. Alternatively, calculating the current first gives

I = \frac{P}{V} = \frac{36}{12} = 3\text{ A}

, and applying Ohm's Law gives

R = \frac{V}{I} = \frac{12}{3} = 4\text{ }\Omega

Step-by-Step Solution

Identify the given values and appropriate power formula relating power (

P

), voltage (

V

), and resistance (

R

P = 36\text{ W}

V = 12\text{ V}

, using

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

This formula directly links the known electrical values to the unknown circuit resistance.

Rearrange the formula to solve for resistance (

R

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

Isolating the unknown variable allows direct calculation.

Substitute the given numerical values and calculate the final resistance.

R = \frac{(12\text{ V})^2}{36\text{ W}} = \frac{144}{36} = 4\text{ }\Omega

Squaring the voltage and dividing by total power yields the resistance in ohms.

Key Concept

Relationship between electrical power, voltage, and resistance in DC circuits

Estimated Time:1m 0s

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