Question

1. a resistor has a power rating of 500 w and has a resistance value of 25 \\(\omega\\). what is the maximum amount of current that can flow through this resistor without exceeding the power rating?

20 amperes

5 amperes

2 amperes

50 amperes

Explanation:

Identify the given values and target unknown

Using the Electric Power Formula knowledge point

$$
LATEXBLOCK0
$$

Relate power, resistance, and current

Using the Electric Power Formula knowledge point

$$
LATEXBLOCK1
$$

Solve for the maximum current

Using the Electric Power Formula knowledge point

$$
LATEXBLOCK2
$$

Match with the closest safe option

The calculated maximum current is approximately \(4.47\text{ A}\). To prevent exceeding the power rating of \(500\text{ W}\), the current must not exceed \(4.47\text{ A}\). Among the given choices:

• \(20\text{ amperes}\) would exceed the rating.
• \(5\text{ amperes}\) would exceed the rating (\(5^2 \times 25 = 625\text{ W}\)).
• \(2\text{ amperes}\) is safe (\(2^2 \times 25 = 100\text{ W}\)) and is the only option below the absolute maximum threshold.
• \(50\text{ amperes}\) would exceed the rating.

Answer:

• 20 amperes
• 5 amperes
• 2 amperes (Correct answer)
• 50 amperes