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": [ "Equivalent Resistance", "Series and Parallel Circuits", "Ohm's Law", "Joule Heating" ], "new_concepts": [], "current_concepts": [ "Equivalent Resistance", "Series and Parallel Circuits", "Ohm's Law", "Joule Heating" ] } ## Calculate the equivalent resistance of the rightmost branch $$ \begin{aligned} R_{\text{right}} &= 470\,\Omega + 680\,\Omega + 570\,\Omega \ R_{\text{right}} &= 1720\,\Omega \end{aligned} $$ ## Calculate the equivalent resistance of the parallel combination $$ \begin{aligned} R_p &= \frac{220 \times 1720}{220 + 1720} \ R_p &= \frac{378400}{1940} \approx 195.0515\,\Omega \end{aligned} $$ ## Calculate the total resistance of the branch containing the 110-ohm resistor $$ \begin{aligned} R_{\text{branch}} &= 110\,\Omega + R_p \ R_{\text{branch}} &= 110\,\Omega + 195.0515\,\Omega = 305.0515\,\Omega \ I_{\text{branch}} &= \frac{V}{R_{\text{branch}}} = \frac{12\,\text{V}}{305.0515\,\Omega} \approx 0.0393376\,\text{A} \ E_{110} &= I_{\text{branch}}^2 \times R \times t \ E_{110} &= (0.0393376\,\text{A})^2 \times 110\,\Omega \times 15\,\text{s} \approx 2.5532\,\text{J} \end{aligned} $$ $2.55\,\text{J}$ { "subject": "Natural Science", "question_type": "Free Response", "knowledge_point": [ "Natural Science", "Physics", "Joule Heating" ] }

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Calculate the equivalent resistance of the rightmost branch

Calculate the equivalent resistance of the parallel combination

Calculate the total resistance of the branch containing the 110-ohm resistor

Answer: