A workshop exhaust fan is connected to a 120\text{ V} power supply and consumes 480\text{ … — Armed Services Vocational Aptitude Battery (ASVAB)

A workshop exhaust fan is connected to a $120\text{ V}$ power supply and consumes $480\text{ W}$ of electric power during normal operation. What is the effective electrical resistance of the fan motor, in ohms ( $\Omega$ )?

Answer: 30 ohms

Answer

The effective electrical resistance of the fan motor is

30\,\Omega

To find the resistance from voltage and power, determine the current using

I = \frac{P}{V} = \frac{480\text{ W}}{120\text{ V}} = 4\text{ A}

, then use Ohm's law

R = \frac{V}{I} = \frac{120\text{ V}}{4\text{ A}} = 30\,\Omega

. Alternatively, using

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

yields

\frac{120^2}{480} = \frac{14400}{480} = 30\,\Omega

Step-by-Step Solution

Calculate the electric current flowing through the fan motor using the electrical power formula

P = V \times I

I = \frac{P}{V} = \frac{480\text{ W}}{120\text{ V}} = 4\text{ A}

Electric power equals the product of voltage and current, so dividing total wattage by applied voltage determines circuit current.

Calculate the resistance using Ohm's law rearranged as

R = \frac{V}{I}

R = \frac{120\text{ V}}{4\text{ A}} = 30\,\Omega

Resistance represents the opposition to current flow and is found by dividing the applied voltage by the circuit current.

Key Concept

Relationship between electrical power (

P = IV

) and Ohm's law (

V = IR

)

Estimated Time:1m 0s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic