Electric and Magnetic Fields: Discharging Capacitors

Electric and Magnetic Fields: Discharging Capacitors

Discharging Capacitors

  • A capacitor is a device used to store electric charge and energy in an electric field.
  • Discharging a capacitor involves the transfer of the stored charge from one plate of the capacitor to the other, done through an external electric circuit.
  • The voltage, current, and charge of a capacitor all change exponentially during the process of discharging.

Time Constants

  • The time constant (τ, tau) of a capacitor is the time taken for the charge or voltage to decrease to about 37% of its initial value, or for the current to decrease to about 0.37 of its initial peak value.
  • It is calculated using the formula τ = RC, where R is the resistance in the circuit and C is the capacitance of the capacitor.
  • The time constant is a measure of how quickly the capacitor discharges.

Current During Discharge

  • The electric current (I) during the discharging process at any time ‘t’ can be given by the equation I = I0 e^(-t/RC) where I0 is the maximum initial current and e is the base of natural logarithms (approximately equal to 2.71828).
  • The current and charge are maximum at the start (t=0) and decrease exponentially with time.

Capacitor Discharge Graphs

  • The discharge curves of a capacitor are exponential decay curves.
  • The voltage vs time, charge vs time, and current vs time graphs are all exponential decays, reflecting the continual decrease of these quantities as the capacitor discharges.
  • At time t = τ, the voltage, charge, and current have reached about 37% of their initial values.

Energy Considerations

  • Energy stored in a fully charged capacitor is given by the equation E = 0.5CV², where C is the capacitance and V is the voltage.
  • During discharging, some of the energy is transferred to other parts of the circuit (resistance), where it is dissipated as heat.
  • After complete discharge, energy stored in the capacitor is zero.

Practical Applications

  • Understanding capacitor discharging is crucial in many areas including electronic filters, defibrillator machines, flash photography, and power supply smoothing.
  • Prolonged time constants are used to store energy for longer periods, such as in emergency lighting systems.