A direct-current (DC) soldering iron operates on a 24\text{ V} power supply and dissipates… — Armed Services Vocational Aptitude Battery (ASVAB)

A direct-current (DC) soldering iron operates on a $24\text{ V}$ power supply and dissipates $72\text{ W}$ of power. What is the electrical resistance of the heating element?

A
$0.33\ \Omega$
$8\ \Omega$ Answer
C
$3\ \Omega$
D
$24\ \Omega$

Answer

8\ \Omega

According to Watt's Law, power dissipated by a resistance is

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

. Solving for resistance gives

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

. Substituting

24\text{ V}

and

72\text{ W}

yields

R = \frac{24^2}{72} = \frac{576}{72} = 8\ \Omega

Step-by-Step Solution

Identify the given values and select the Watt's Law formula that relates voltage, power, and resistance.

V = 24\text{ V}

P = 72\text{ W}

, and

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

The circuit voltage and power dissipation are known, and the resistance is the target variable.

Rearrange the formula to isolate resistance (

R

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

Multiplying both sides by

R

and dividing by

P

provides the direct expression for resistance.

Square the voltage and divide by the power to find the resistance in ohms.

R = \frac{24^2}{72} = \frac{576}{72} = 8\ \Omega

Evaluating the numerical expression yields the final resistance value.

Key Concept

Watt's Law relates power, voltage, and resistance through the relationship

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

, which can be rearranged as

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

Estimated Time:1m 0s

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Step-by-Step Solution

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