A system of four capacitors is connected across a 90-V voltage source as shown in the figure. What is the equivalent capacitance of this system?

Question

BlackTom AI · Accepted Answer

To analyze the network, first identify the topology: there are two branches connected in parallel across the 90 V source, with each branch containing capacitors in series.
Option A: 3.9 μF. If someone mistakenly treated the entire network as a single combined series or miscalculated the parallel combination, they might arrive at 3.9 μF, but that value does not match the correct two-branch calculation.
Option B: 3.6 μF. This could arise from rounding errors or misapplication of formulas (e.g., averaging branch values) rather than a proper series-parallel combination. The exact result from correct analysis is not 3.6 μF.
Option C: 1.5 μF. This is roughly the result you would get if you incorrectly treated the two series branches as if they were in series with each other, or if you scaled one branch wrongly. The actual equivalent is larger because the branches are in parallel, not in series.
Option D: 3.3 μF. This is the correct magnitude once the two branches are handled correctly: compute each branch’s series equivalent, then add in parallel.
Option E: 15 μF. This would require a drastic overestimation, such as misplacing units or treating the setup as multiple direct connections of capacitances in a way that ignores the series restrictions. It is not consistent with the given network.
Detailed analysis:
- Top branch: the 2.0 μF and 4.0 μF capacitors are in series. The equivalent is (2.0 × 4.0) / (2.0 + 4.0) = 8.0 / 6.0 = 1.333… μF.
- Bottom branch: the 3.0 μF and 6.0 μF capacitors are in series. The equivalent is (3.0 × 6.0) / (3.0 + 6.0) = 18.0 / 9.0 = 2.0 μF.
- The two branches are connected in parallel, so the total equivalent capacitance is the sum: 1.333… μF + 2.0 μF = 3.333… μF, which rounds to 3.3 μF.
Therefore, the correct overall capacitance is 3.3 μF, and the other options arise from common but incorrect misapplications of series/parallel rules or arithmetic rounding.

A system of four capacitors is connected across a 90-V voltage source as shown in the figure. What is the equivalent capacitance of this system? 单项选择题

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