Final answer:
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.