SUMMARY
The problem involves calculating the capacitance of two 5.0-cm-diameter aluminum electrodes spaced 0.50 mm apart and connected to a 200 V battery. The correct formula for capacitance is C = εA/d, where ε is the permittivity of free space (8.85 x 10^-12 F/m), A is the area of the electrodes, and d is the distance between them. The area was calculated using the formula A = π(d^2)/4, leading to a capacitance of approximately 139 pF. The initial calculation error stemmed from incorrect area computation.
PREREQUISITES
- Understanding of capacitance and the formula C = εA/d
- Knowledge of the geometry of circular electrodes
- Familiarity with basic electrical concepts such as voltage and charge
- Ability to perform unit conversions (e.g., cm to m)
NEXT STEPS
- Review the derivation of the capacitance formula C = εA/d
- Learn about the effects of dielectric materials on capacitance
- Explore the concept of electric field strength between parallel plates
- Investigate practical applications of capacitors in electronic circuits
USEFUL FOR
Students in electrical engineering, physics enthusiasts, and anyone studying capacitor design and calculations.