what is the total resistance of the following circuit?

$487\ \omega$
$114\ \omega$
$259\ \omega$
$414\ \omega$

Question

what is the total resistance of the following circuit?

$487\ \omega$
$114\ \omega$
$259\ \omega$
$414\ \omega$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Equivalent Resistance", "Series and Parallel Circuits" ], "new_concepts": [], "current_concepts": [ "Equivalent Resistance", "Series and Parallel Circuits" ] } ## Identify the circuit configuration Using the *Series and Parallel Circuits* knowledge point $$ \begin{aligned} &R_2 = 170\ \Omega \ &R_3 = 133\ \Omega \ &R_{23} = \frac{R_2 \cdot R_3}{R_2 + R_3} \ &R = 184\ \Omega \ &R_{\text{total}} = R + R_{23} \end{aligned} $$ ## Calculate the parallel equivalent resistance Using the *Equivalent Resistance* knowledge point $$ \begin{aligned} &R_{23} = \frac{170 \cdot 133}{170 + 133} \ &R_{23} = \frac{22610}{303} \approx 74.62\ \Omega \end{aligned} $$ ## Calculate the total equivalent resistance Using the *Equivalent Resistance* knowledge point $$ \begin{aligned} &R_{\text{total}} = 184 + 74.62 \ &R_{\text{total}} \approx 258.62\ \Omega \approx 259\ \Omega \end{aligned} $$

$487\ \Omega$

$114\ \Omega$

$259\ \Omega$

$414\ \Omega$

{ "subject": "Natural Science", "question_type": "Multiple Choice", "knowledge_point": [ "Natural Science", "Physics", "Equivalent Resistance" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the circuit configuration

Calculate the parallel equivalent resistance

Calculate the total equivalent resistance

Answer: