How to Calculate the Capacitance of a Capacitor and the Charge on Its Plates?

To calculate the capacitance of a parallel plate capacitor, we can use the formula:

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 of the plates in square meters (m²)
• d = distance between the plates in meters (m)

Given:

• Plate dimensions: 20 cm x 30 cm = 0.2 m x 0.3 m
• Distance between plates: 10 mm = 0.01 m
• Voltage (V) = 12 V

Now, let’s calculate the area (A):

A = 0.2 m * 0.3 m = 0.06 m²

Now, substitute into the capacitance formula:

C = 8.854 x 10^-12 F/m * (0.06 m² / 0.01 m)

C = 8.854 x 10^-12 F/m * 6 = 5.3124 x 10^-11 F

So, the capacitance is approximately 53.124 pF (picoFarads).

Next, to find the charge (Q) on each plate, we use the formula:

Q = C * V

Substituting our known values:

Q = 5.3124 x 10^-11 F * 12 V

Q = 6.37488 x 10^-10 C

Rounded to three significant figures, the charge on each plate is approximately 637 pC (picoCoulombs).