Capacitors

• Capacitor symbol


  Two parallel lines
• Charging a capacitor


  1. Electrons flow from negative terminal of cell to negative plate of capacitor

  2. Excess electrons gather on negative plate

  3. Electrons on positive plate move towards positive terminal of cell
• Capacitance


  Amount of charge stored per unit of potential difference
• Capacitance formula


  c = q/v
• Discharging a capacitor


  1. Excess electrons flow from negative plate to positive plate

  2. Charge on capacitor decreases
• Capacitors in parallel


  • Total capacitance = sum of individual capacitances
• In a parallel circuit, the voltage is the same across all branches
• In a series circuit, the charge is the same across all capacitors
• Exponential decay equation for capacitor discharge

  v = v_0 * e^(-t/(CR))
• Time constant


  τ = CR, time for voltage to drop to 37% of initial value
• Deriving time for capacitor discharge

  1. ln(v/v_0) = -t/(CR)

  2. t = CR * ln(v_0/v)
• Exponential functions have a constant ratio between values in equal time intervals
• Time constant τ = CR
• At time t = τ, voltage drops to 37% of initial value
• Determining capacitance from discharge graph

  1. Time constant τ = 25s

  2. Resistance R = 5kΩ

  3. Capacitance C = τ/R = 25/5000 = 5μF
• Charging a capacitor


  1. Voltage across resistor decreases exponentially

  2. Voltage across capacitor increases as v_c = v_0(1 - e^(-t/(CR)))

  3. Current decreases exponentially as i = i_0 * e^(-t/(CR))