Question

Physical Characteristics of Capacitors *P3.31. Determine the capacitance of a parallel-plate capacitor having plates 100 mm by 0.3 m separated by 0.04 mm. The dielectric constant ϵ=100pF/m

Answer 1

To calculate the capacitance of a parallel-plate capacitor, you need to know the area of the plates, the separation between them, and the dielectric constant. By applying the formula C = ε₀(εr)(A/d) with the given values and measurements converted to meters, we find that the capacitance is approximately 66.375 pF.

Step-by-step explanation:

To determine the capacitance of a parallel-plate capacitor, we use the formula:

C = ε₀(εr)(A/d)

Where:

• C is the capacitance,
• ε₀ is the permittivity of free space (8.85 × 10-12 F/m),
• εr is the relative permittivity or dielectric constant,
• A is the area of the plates,
• d is the separation between the plates.

Given that the plates are 100 mm by 0.3 m and separated by 0.04 mm with a dielectric constant of 100 pF/m, we first convert all measurements to meters:

• 100 mm = 0.1 m
• 0.04 mm = 0.04 × 10-3 m

Now we calculate the area A:

• A = 0.1 m × 0.3 m = 0.03 m2

Plugging in the values:

C = (8.85 × 10-12 F/m)(100 × 10-12 F/m)(0.03 m2) / (0.04 × 10-3 m)

C = 66.375 × 10-15 F

So, the capacitance is approximately 66.375 pF. Thus, you can calculate the required characteristics of capacitors using formulas and conversions to standard units.