determine the energy dissipated by the 110-ohm resistor in 15 seconds.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Series Circuits", "Parallel Circuits", "Equivalent Resistance", "Ohms Law" ], "new_concepts": [ "Joule Heating", "Electric Energy Dissipation" ], "current_concepts": [ "Series Circuits", "Parallel Circuits", "Equivalent Resistance", "Ohms Law", "Electric Energy Dissipation" ] } ## Calculate equivalent resistance of the rightmost branch $$ R_{\text{right}} = 470\,\Omega + 680\,\Omega + 570\,\Omega = 1720\,\Omega $$ ## Calculate equivalent resistance of the parallel combination with the $220\,\Omega$ resistor $$ R_{p} = \frac{220 \times 1720}{220 + 1720} = \frac{378400}{1940} \approx 195.05154639\,\Omega $$ ## Calculate equivalent resistance of the branch containing the $110\,\Omega$ resistor $$ R_{\text{branch}} = 110\,\Omega + R_{p} = 110 + 195.05154639 = 305.05154639\,\Omega $$ ## Calculate current and energy dissipated by the $110\,\Omega$ resistor $$ \begin{aligned} I_{\text{branch}} &= \frac{12\,\text{V}}{R_{\text{branch}}} = \frac{12}{305.05154639} \approx 0.039337613\,\text{A} \ P_{110} &= I_{\text{branch}}^2 \times 110 \approx (0.039337613)^2 \times 110 \approx 0.170219\,\text{W} \ E_{110} &= P_{110} \times t = 0.170219 \times 15 \approx 2.553285\,\text{J} \end{aligned} $$ $2.55\,\text{J}$ { "subject": "Natural Science", "question_type": "Free Response", "knowledge_point": [ "Natural Science", "Physics", "Electric Energy Dissipation" ] }

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Explanation:

Calculate equivalent resistance of the rightmost branch

Calculate equivalent resistance of the parallel combination with the \(220\,\Omega\) resistor

Calculate equivalent resistance of the branch containing the \(110\,\Omega\) resistor

Calculate current and energy dissipated by the \(110\,\Omega\) resistor

Answer: