Dependence of the Capacitance of a Capacitor

Overview

The capacitance of a capacitor depends on three factors, demonstrated through an experiment using two plates (A and B) connected to a gold-leaf electroscope.

Factor 1 — Area of the Plates

• In the experiment, plates A and B are connected to a gold-leaf electroscope, and the overlapping area between the plates is reduced.
• Observation: Reducing the overlapping area increases the divergence of the electroscope leaves (i.e., the potential difference increases for the same charge).
• Conclusion: Capacitance is directly proportional to the area of the plates.
• Relation: C ∝ A

Factor 2 — Distance Between the Plates

• The distance between plates A and B is reduced while keeping the charge constant.
• Observation: Reducing the distance decreases the divergence of the electroscope leaves (i.e., the potential difference decreases).
• Conclusion: Capacitance is inversely proportional to the distance between the plates.
• Relation: C ∝ \[\frac {1}{d}\]

Factor 3 — Medium Between the Plates (Dielectric)

• An insulating material — such as glass, mica, paraffin wax, or oil — is inserted between the plates while keeping the distance constant.
• Observation: Inserting the dielectric decreases the divergence of the electroscope leaves.
• Conclusion: Capacitance is directly proportional to the dielectric constant (K) of the medium.
• Relation: C ∝ K

• Capacitance ∝ Area of plates (A)
• Capacitance ∝ 1 / Distance between plates (d)
• Capacitance ∝ Dielectric constant (K) of the medium
• All three relationships demonstrated using a gold-leaf electroscope experiment