Two 4.0-Ω resistors are connected in parallel, and this combination is connected in series with 3.0 Ω. What is the equivalent resistance of this system?

Question

Two 4.0-Ω resistors are connected in parallel, and this combination is connected in series with 3.0 Ω.  What is the equivalent resistance of this system?

BlackTom AI · Accepted Answer

When resistors are in parallel, their combined resistance is found using the formula 1/Rp = 1/R1 + 1/R2. Here, both resistors have R1 = R2 = 4.0 Ω, so Rp = 1 / (1/4 + 1/4) = 1 / (1/2) = 2.0 Ω. Next, this parallel combination is placed in series with a 3.0 Ω resistor. In a series arrangement, resistances simply add, so Rtotal = Rp + 3.0 Ω = 2.0 Ω + 3.0 Ω = 5.0 Ω.

Now, evaluate the given options:
- Option 11 Ω: This would imply either a misapplication of the parallel formula or an incorrect addition in series. It does not match the parallel result of 2.0 Ω nor the final sum of 5.0 Ω, so it is inaccurate for this configuration.
- Option 7.0 Ω: If someone mistakenly added the parallel result (2.0 Ω) to a different value or treated the parallel pair as a single 4.0 Ω in series, they might arrive at 6.0 Ω or 7.0 Ω through arithmetic errors. However, the correct series sum with 3.0 Ω is 5.0 Ω, not 7.0 Ω.
- Option 5.0 Ω: This exactly matches the computed total resistance when the parallel pairing (2.0 Ω) is added in series with 3.0 Ω, yielding 5.0 Ω. It aligns with both the parallel and series rules.
- Option 1.2 Ω: A value this small could result from miscalculating the parallel combination (e.g., treating them as if they were in series) or mixing units, but it does not reflect the correct parallel-in-series sequence for 4.0 Ω resistors.

In summary, applying the correct parallel formula to the two 4.0 Ω resistors gives 2.0 Ω, and adding the 3.0 Ω in series yields a total of 5.0 Ω. The other options reflect common arithmetic or conceptual mistakes, such as misdoing the parallel step or misplacing the series addition.

Two 4.0-Ω resistors are connected in parallel, and this combination is connected in series with 3.0 Ω. What is the equivalent resistance of this system?单项选择题

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