9. a series circuit has an applied total voltage of 240 volts. at one of the resistors, the voltage drop is measured at 48 volts, and the power at that resistor is measured at 96 watts. what is the total resistance in the circuit?

120 $\omega$

480 $\omega$

240 $\omega$

Question

9. a series circuit has an applied total voltage of 240 volts. at one of the resistors, the voltage drop is measured at 48 volts, and the power at that resistor is measured at 96 watts. what is the total resistance in the circuit?

120 $\omega$

480 $\omega$

240 $\omega$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Series Circuits", "Electric Current", "Voltage Drop", "Ohms Law" ], "new_concepts": [ "Electric Power Formula" ], "current_concepts": [ "Series Circuits", "Electric Current", "Voltage Drop", "Ohms Law", "Electric Power Formula" ] } ## Calculate the current through the resistor $$ \begin{aligned} P_1 &= 96\text{ W}\ V_1 &= 48\text{ V}\ I &= \frac{P_1}{V_1} = \frac{96\text{ W}}{48\text{ V}} = 2\text{ A} \end{aligned} $$ ## Calculate the total resistance of the series circuit $$ \begin{aligned} V_{\text{total}} &= 240\text{ V}\ I_{\text{total}} &= I = 2\text{ A}\ R_{\text{total}} &= \frac{V_{\text{total}}}{I_{\text{total}}} = \frac{240\text{ V}}{2\text{ A}} = 120\ \Omega \end{aligned} $$

(A) 120 $\Omega$

(B) 480 $\Omega$

(C) 240 $\Omega$

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

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Question

Explanation:

Calculate the current through the resistor

Calculate the total resistance of the series circuit

Answer: