A variable air capacitor has 10 movable plate and 11stationary plates. The area of each plate is 0.002 M2 and separation between opposite plates is 0.001m. Determine the maximum capacitance of this variable capacitor.

To determine the maximum capacitance of a variable air capacitor with the given specifications, we can use the formula for capacitance, which is defined as:

Capacitance Formula

The capacitance (C) of a capacitor is given by the equation:

C = ε₀ * (A/d)

Where:

• C = capacitance in farads (F)
• ε₀ = permittivity of free space (approximately 8.854 x 10^-12 F/m)
• A = area of one plate in square meters (m²)
• d = separation between the plates in meters (m)

Calculating Maximum Capacitance

In this case, we have 10 movable plates and 11 stationary plates. The maximum capacitance occurs when all movable plates are fully engaged with the stationary plates. This means that each movable plate can connect with a stationary plate, creating a total of 10 capacitors in parallel.

First, we need to calculate the effective area (A) for one capacitor. Since each plate has an area of 0.002 m², and there are 10 movable plates, the total area for one capacitor is:

A = 0.002 m²

The separation (d) between the plates is given as 0.001 m. Now, substituting these values into the capacitance formula:

Substituting Values

C = ε₀ * (A/d)

C = (8.854 x 10^-12 F/m) * (0.002 m² / 0.001 m)

C = (8.854 x 10^-12 F/m) * 0.002 m

C = 1.7708 x 10^-14 F

Considering All Capacitors in Parallel

Since we have 10 such capacitors in parallel, the total capacitance (C_total) is simply 10 times the capacitance of one capacitor:

C_total = 10 * C

C_total = 10 * (1.7708 x 10^-14 F)

C_total = 1.7708 x 10^-13 F

Final Result

The maximum capacitance of the variable air capacitor is approximately 1.77 x 10^-13 F, or 177 pF (picoFarads).

This calculation illustrates how the configuration of plates and their area directly influences the capacitance of a capacitor. Understanding these principles is crucial in designing and utilizing capacitors in various electronic applications.