a transformer has a secondary voltage of 144 volts and a secondary current of 2.5 amps. if the primary current is 12 amps, what is the primary voltage? (in this case, the voltages and currents are inversely proportional.)

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Transformer Voltage Ratio", "Inverse Proportion Equations" ], "new_concepts": [], "current_concepts": [ "Transformer Voltage Ratio", "Inverse Proportion Equations" ] } ## Set up the inverse proportion equation $$ V_p \cdot I_p = V_s \cdot I_s $$ ## Substitute the given values $$ \begin{aligned} V_s &= 144\text{ V} \ I_s &= 2.5\text{ A} \ I_p &= 12\text{ A} \ V_p \cdot 12 &= 144 \cdot 2.5 \end{aligned} $$ ## Solve for the primary voltage $$ \begin{aligned} 12 \cdot V_p &= 360 \ V_p &= 30\text{ V} \end{aligned} $$ $30\text{ volts}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Inverse Proportion Equations" ] }

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Explanation:

Set up the inverse proportion equation

Substitute the given values

Solve for the primary voltage

Answer: