8. a resistor has a power rating of 1000 w and is connected to an applied voltage of 120 v. what is the minimum resistance value of this resistor to stay operating within the power rating?

1000 $\omega$

144 $\omega$

14.4 $\omega$

28.8 $\omega$

Question

8. a resistor has a power rating of 1000 w and is connected to an applied voltage of 120 v. what is the minimum resistance value of this resistor to stay operating within the power rating?

1000 $\omega$

144 $\omega$

14.4 $\omega$

28.8 $\omega$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Electric Power Formula" ], "new_concepts": [], "current_concepts": [ "Electric Power Formula", "Electrical Resistance" ] } ## Identify the given parameters Using the *Electric Power Formula* knowledge point $$ \begin{aligned} &P_{\text{max}} = 1000\text{ W}\ &V = 120\text{ V} \end{aligned} $$ ## Relate power, voltage, and resistance Using the *Electric Power Formula* knowledge point $$ \begin{aligned} &P = \frac{V^2}{R}\ &R = \frac{V^2}{P} \end{aligned} $$ ## Calculate the minimum resistance Using the *Electric Power Formula* knowledge point $$ \begin{aligned} &R_{\text{min}} = \frac{120^2}{1000}\ &R_{\text{min}} = \frac{14400}{1000} = 14.4\ \Omega \end{aligned} $$

(A) $1000\ \Omega$

(B) $144\ \Omega$

(C) $14.4\ \Omega$

(D) $28.8\ \Omega$

{ "subject": "Natural Science", "question_type": "Multiple Choice", "knowledge_point": [ "Natural Science", "Physics", "Electric Power Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given parameters

Relate power, voltage, and resistance

Calculate the minimum resistance

Answer: