A direct-current (DC) avionics heating resistor with a resistance of 200\ \Omega dissipate… — Armed Services Vocational Aptitude Battery (ASVAB)

A direct-current (DC) avionics heating resistor with a resistance of $200\ \Omega$ dissipates $18\text{ W}$ of electrical power under steady-state operating conditions. What is the magnitude of the current flowing through the resistor?

A
$90\text{ mA}$
$300\text{ mA}$ Answer
C
$0.30\text{ mA}$
D
$60\text{ mA}$

Answer

300\text{ mA}

According to Watt's Law, power dissipation in a resistive load is given by

P = I^2 R

. Rearranging to solve for current gives

I = \sqrt{\frac{P}{R}} = \sqrt{\frac{18\text{ W}}{200\ \Omega}} = \sqrt{0.09\text{ A}^2} = 0.3\text{ A}

. Multiplying by

1{}000

converts the current to

300\text{ mA}

Step-by-Step Solution

Select the appropriate Watt's Law formula that relates power (

P

), current (

I

), and resistance (

R

P = I^2 R

The known quantities are electrical power (

18\text{ W}

) and resistance (

200\ \Omega

), and the target quantity is current (

I

Rearrange the formula to solve for the squared current (

I^2

I^2 = \frac{P}{R} = \frac{18\text{ W}}{200\ \Omega} = 0.09\text{ A}^2

Isolating the variable term allows direct computation of

I^2

Take the square root of both sides to calculate the current in amperes (

A

I = \sqrt{0.09\text{ A}^2} = 0.3\text{ A}

Current is the square root of

I^2

Convert the current from amperes (

A

) to milliamperes (

\text{mA}

0.3\text{ A} \times 1{}000\text{ mA/A} = 300\text{ mA}

Expressing the value in standard sub-unit milliamperes.

Key Concept

Watt's Law relates power, current, and resistance through the formula

P = I^2 R

, which can be rearranged as

I = \sqrt{\frac{P}{R}}

Estimated Time:1m 0s

Question

Answer

Step-by-Step Solution

Key Concept

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