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Circuit and electromagnetism basics

In a parallel-plate capacitor, if the plate area is doubled and the plate spacing is halved, by what factor does the capacitance change? (The dielectric between the plates is unchanged.)

  1. A1 (unchanged)
  2. B4 times
  3. C2 times
Show answer and explanation

Answer: B. 4 times

A parallel-plate capacitor has C = εS/d (ε: permittivity, S: plate area, d: spacing), proportional to area and inversely proportional to spacing. Doubling the area doubles it, and halving the spacing doubles it again, for 2 × 2 = 4 times in total. Filling the gap with a dielectric of relative permittivity εr multiplies the capacitance by εr. Multilayer ceramic capacitors stack many thin dielectric layers to reach large capacitances.

  • A. Increasing the area and narrowing the gap both increase capacitance; they do not cancel.
  • B. Correct. 2 × 2 = 4 times.
  • C. 2 times accounts for only one of the two changes.
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