Question number 54 on page 718 of your text book (this is a review question) shows a compound circuit. It has a 10 volt battery with two 30 ohm resistors in parallel connected to a 5 ohm resistor in series with them. What is the equivalent resistance of the whole circuit. You can assume the battery has no internal resistance.

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BlackTom AI · Accepted Answer

Question restatement: A circuit has a 10 V battery (assumed with no internal resistance) connected to two 30 Ω resistors in parallel, and that parallel network is in series with a 5 Ω resistor. The task is to find the equivalent resistance of the entire circuit.

Option analysis:
Option A: 'boarders sometimes think of Stevenson as their ohm away from ohm' This choice is nonsensical in this physics context and does not provide a numerical resistance value or a valid reasoning path related to series/parallel combinations.

Option B: '20 ohms' This is the correct calculation outcome. First compute the parallel part: R_parallel = (R1 * R2) / (R1 + R2) = (30 * 30) / (30 + 30) = 900 / 60 = 15 Ω. Then add the series resistor: R_total = R_parallel + R_series = 15 Ω + 5 Ω = 20 Ω. So the equivalent resistance of the whole circuit is 20 Ω.

Option C: '65 ohms' This would imply either misapplying the parallel formula or misadding in a way that ignores the actual network. If you attempted to sum all resistors (30 + 30 + 5), you’d get 65 Ω, but that ignores that the two 30 Ω resistors are in parallel, not in series with each other.

Option D: '35 ohms' This result might come from incorrectly combining parts, such as treating the 30 Ω resistors as parallel to yield 15 Ω and then adding 5 Ω to get 20 Ω, but if a student mistakenly uses a different wrong parallel or series arrangement, they could end up with 35 Ω. However, the correct sequence (parallel first, then series) does not yield 35 Ω.

Summary: The only value consistent with the actual network reduction—parallel combination of the two 30 Ω resistors yielding 15 Ω, followed by adding the 5 Ω in series—gives 20 Ω. The other options arise from common misapplications of the series/parallel rules or from irrelevant or incorrect interpretations.

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