Charging & Discharging a Capacitor

Introduction

• Capacitors are components in electrical circuits that can store electric charge.
• Investigating the charge and discharge of a capacitor is essential for understanding its behaviour in circuits.

The Circuit Setup

• The circuit used to study charging and discharging consists of a voltage source (E) in series with a capacitor, resistor (R), ammeter, and a two-way switch.
• The supply has negligible internal resistance.

Charging a Capacitor

• Initially, the capacitor is uncharged.
• When the switch is in position 1, electrons flow from the negative terminal of the supply to the lower plate of the capacitor.
• The initial current (I) in the circuit during charging is given by I = E/R.
• Key points during charging:
  • Charging current decreases from E/R to zero.
  • The potential difference (V) across the capacitor plates increases from zero to E when fully charged.
  • The sum of the potential difference across the capacitor and resistor always equals the EMF (E) of the supply.
  • The potential difference across the resistor (given by VR = IR) decreases from E to zero when fully charged.

Discharging a Capacitor

• Initially, the capacitor is fully charged.
• When the switch is in position 2, electrons flow from the lower plate through the resistor to the upper plate of the capacitor.
• The initial discharging current (I) is -E/R.

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Physics

Charging & Discharging a Capacitor from a d.c. Source

• Key points during discharging:
  • Discharging current decreases from -E/R to zero.
  • The potential difference across the capacitor plates decreases from E to zero when fully discharged.
  • The potential difference across the capacitor always equals the potential difference across the resistor (VR).
  • The potential difference across the resistor (VR) decreases from E to zero when fully discharged.

Summary

• Charging a capacitor involves electrons moving from the supply to the capacitor, while discharging involves electrons moving from the capacitor through the resistor.
• During charging, the current decreases, and the potential difference across the capacitor plates increases.
• During discharging, the current also decreases, and the potential difference across the capacitor plates decreases.
• The potential difference across the capacitor and resistor always obeys Ohm's Law, and their sum is equal to the supply's EMF.
• Understanding these processes is crucial for designing circuits and using capacitors effectively.