determine the overall current in the circuit. (assume 2 sig figs for the values below.)

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Equivalent Resistance", "Series and Parallel Circuits", "Ohm's Law" ], "new_concepts": [], "current_concepts": [ "Equivalent Resistance", "Series and Parallel Circuits", "Ohm's Law" ] } ## Calculate the equivalent resistance of the parallel circuit $$ \begin{aligned} \frac{1}{R_{eq}} &= \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \ \frac{1}{R_{eq}} &= \frac{1}{300\ \Omega} + \frac{1}{100\ \Omega} + \frac{1}{200\ \Omega} \ \frac{1}{R_{eq}} &= \frac{2 + 6 + 3}{600\ \Omega} = \frac{11}{600\ \Omega} \ R_{eq} &= \frac{600}{11}\ \Omega \approx 54.55\ \Omega \end{aligned} $$ ## Calculate the overall current using Ohm's law $$ \begin{aligned} I &= \frac{V}{R_{eq}} \ I &= \frac{9.0\text{ V}}{\frac{600}{11}\ \Omega} \ I &= \frac{99}{600}\text{ A} = 0.165\text{ A} \end{aligned} $$ ## Apply significant figures rounding $$ I \approx 0.17\text{ A} $$ $0.17\text{ A}$ { "subject": "Natural Science", "question_type": "Free Response", "knowledge_point": [ "Natural Science", "Physics", "Series and Parallel Circuits" ] }

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Explanation:

Calculate the equivalent resistance of the parallel circuit

Calculate the overall current using Ohm's law

Apply significant figures rounding

Answer: