Capacitors and Capacitance: Study Notes for IIT JEE

What is a Capacitor?

• A capacitor (also known as an electric condenser) is a two-terminal electrical component designed to store energy in the form of an electric charge.
• Capacitance varies from small to high storage.

Capacitance in Physics

• Capacitance is the ability of a capacitor to store energy as an electric charge, measured in farads.
• Example: A capacitor storing 9 coulombs with a 9V battery has a capacitance of 1 farad.

Construction of a Capacitor

• Consists of two electrical conductors separated by a dielectric or between metallic plates.
• Conductors can be electrolytes, thin films, or sintered beads of metal.

Role of Non-Conducting Dielectric in Capacitors

• Dielectrics increase the capacitor's ability to charge.
• Common dielectrics: Mica, plastic film, glass, paper, ceramic.

Addition of Capacitors

• Capacitors can be added:
  • In Series: Total capacitance is less than any single capacitor.
  • In Parallel: Total capacitance is the sum of all capacitors.

Capacitor Rating

• Different capacitors can have the same capacitance but different voltage ratings.
• Voltage ratings are important to avoid damage due to excessive voltage.
• Common DC voltage ratings: 10V - 1000V.

Properties or Characteristics of Capacitors

• Nominal Capacitance (C) - Measured in pF, nF, or micro-Farads.
• Working Voltage (WV) - The maximum applied voltage without failure.
• Tolerance (%) - Variability in capacitance value.
• Leakage Current - Small DC current flow, leading to gradual discharge.

Super Capacitors

• Also known as Electric Double-Layer Capacitors (EDLC), Supercaps, Ultracapacitors, or Goldcaps.
• Higher capacitance but lower voltage limits.

Parallel Plate Capacitor

• Consists of two parallel conductive plates with a dielectric between them.
• Capacitance depends on the dielectric material.

Effect of Dielectric on Capacitance

• Dielectric increases capacitance.
• A dielectric constant (K) measures this effect.

Energy Stored in a Capacitor

• Work done moving charge against repulsion is stored as energy.
• Formula involves capacitance and voltage.

Numerical Examples

1. Series Connection: Calculate total capacitance using provided formulas.
2. Parallel Connection: Add capacitances directly.
3. Capacitors with Given Area and Voltage: Use area and separation to find capacitance.
4. Energy Storage Changes: Analyze changes when altering plate distances or connections.

Further Reading

• Capacitors and Capacitance