Final answer:
The capacitance of a parallel-plate capacitor with circular plates 30 cm in radius and separated by 2.4 mm is 1.04 picofarads. This calculation involves finding the area of the plates using the formula for the area of a circle and applying the formula for capacitance of a parallel-plate capacitor.
Step-by-step explanation:
To find the capacitance of a parallel-plate capacitor with circular plates, you can use the formula:
C = ε0 (εr A)/d
Where:
- C is the capacitance,
- ε0 is the vacuum permittivity (8.85 × 10-12 F/m),
- εr is the relative permittivity (for air or vacuum, εr = 1),
- A is the area of one of the plates,
- d is the separation distance between the plates.
First, calculate the area (A) using the radius (r) of the circular plates:
A = π × r2
A = π × (0.3 m)2
A = 0.283 m2
Now, use the area and the given separation distance to calculate the capacitance:
C = 8.85 × 10-12 F/m × (0.283 m2) / (2.4 × 10-3 m)
C = 1.04 × 10-12 F, or 1.04 pF
To express this in picofarads (pF), you merely state the numerical value as it is already in pF by definition.
The capacitance of the parallel-plate capacitor is 1.04 picofarads.