Figure 25-29 shows a variable "air gap" capacitor for manual...

Figure 25-29 shows a variable "air gap" capacitor for manual tuning. Alternate plates are connected together; one group of plates is fixed in position, and the other group is capable of rotation. Consider a capacitor of $n=8$ plates of alternating polarity, each plate having area $A=1.50 \mathrm{~cm}^{2}$ and separated from adjacent plates by distance $d=3.40 \mathrm{~mm}$. What is the maximum capacitance of the device?

Key Concepts

Unit Conversion and Consistency in SI Units

Accurate calculations in physics, particularly in capacitor design, depend on using consistent units. This involves converting areas from units like cm² to m² and distances from mm to m to ensure that the formula for capacitance (which relies on SI units) yields correct and usable results. Consistency in units is fundamental to precise quantitative analysis in electromagnetism.

Multi-Plate Capacitor Configuration

In devices where multiple plates are arranged with alternating connections (such as connecting alternate plates to common terminals), the individual capacitances between each adjacent pair of plates contribute to the overall device capacitance. When configured such that all gaps see the same potential difference, the capacitances add in parallel, leading to a sum of the individual capacitor contributions. This configuration requires a clear understanding of how connections modify series and parallel combinations of capacitors.

Parallel Plate Capacitor

This concept involves understanding that the capacitance of a parallel plate capacitor is given by the formula C = ??A/d, where ?? is the permittivity of free space, A is the area of one plate, and d is the separation between the plates. It represents how the geometry of the capacitor influences its ability to store charge, which is fundamental in electrostatics.

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