What is the maximum current carrying capacity of a resistor of 5000 ohms, 200 watts?

What is the maximum current carrying capacity of a resistor of 5000 ohms, 200 watts?

• A. 0.2 A
• B. 1 A
• C. 1.2 A
• D. None of the above

Answer: (A)

To determine the maximum current carrying capacity of a resistor, Ohm's Law and the power formula can be used. The power in watts (P) can be related to the resistance (R) and current (I) using the formula: \[ P = I^2 \times R. \] In this case, the resistor has a resistance of 5000 ohms and a power rating of 200 watts. Rearranging the formula to find the current gives: \[ I^2 = \frac{P}{R} \] Substituting in the values provided: \[ I^2 = \frac{200}{5000} \] Calculating this yields: \[ I^2 = 0.04 \] Taking the square root of both sides to solve for I gives: \[ I = \sqrt{0.04} = 0.2 \text{ A}. \] This means that the maximum current carrying capacity of the resistor is 0.2 amperes. This value is critical because exceeding this current could lead to the resistor overheating and potentially failing. Therefore, selecting the answer that states 0.2 A accurately reflects the maximum current the resistor can safely handle based on its specifications.

To determine the maximum current carrying capacity of a resistor, Ohm's Law and the power formula can be used. The power in watts (P) can be related to the resistance (R) and current (I) using the formula:

[ P = I^2 \times R. ]

In this case, the resistor has a resistance of 5000 ohms and a power rating of 200 watts. Rearranging the formula to find the current gives:

[ I^2 = \frac{P}{R} ]

Substituting in the values provided:

[ I^2 = \frac{200}{5000} ]

Calculating this yields:

[ I^2 = 0.04 ]

Taking the square root of both sides to solve for I gives:

[ I = \sqrt{0.04} = 0.2 \text{ A}. ]

This means that the maximum current carrying capacity of the resistor is 0.2 amperes. This value is critical because exceeding this current could lead to the resistor overheating and potentially failing. Therefore, selecting the answer that states 0.2 A accurately reflects the maximum current the resistor can safely handle based on its specifications.