Charge and Discharge Equations

• What is the purpose of the time constant in capacitor discharge equations?

  It determines current, charge, or p.d decay

  
• How does the exponential decay affect the charge on a discharging capacitor?

  It determines the remaining charge over time

  
• What does the equation for current in a discharging capacitor indicate about the initial current?

  It affects the rate of discharge

  
• What does the symbol e represent in the context of exponential decay?

  The exponential constant, approximately 2.718
• What is the relationship between current and time constant τ in a discharging capacitor?

  Smaller τ leads to quicker current decay

  
• What is the equation for current in a discharging capacitor?

  I = I₀ e^(-t/τ)

  
• What does Q represent in the capacitor discharge equation?

  Charge on the capacitor plates (C)

  
• How does the charge on a capacitor change over time during discharge?

  It decreases exponentially over time

  
• What is the equation for potential difference in a discharging capacitor?

  V = V₀ e^(-t/τ)

  
• What is the maximum charge stored on a capacitor denoted as?

  Q₀
• What is the relationship between charge and potential difference in a capacitor?

  Charge is directly proportional to potential difference
• What is the approximate value of the exponential constant e?

  Approximately 2.718
• What is the inverse function of e?

  ln(y), the natural logarithmic function
• How do you calculate the time constant τ for a capacitor?

  τ = R × C

  
• If a capacitor has an initial current of 0.6 A and discharges to 0.4 A, what does this indicate?

  The capacitor is losing charge over time

  
• What happens to the charge on a capacitor as it charges over time?

  It increases but at a slower rate

  
• What is the equation for charge on a charging capacitor?

  Q = Q₀ (1 - e^(-t/τ))

  
• What is the equation for potential difference across a charging capacitor?

  V = V₀ (1 - e^(-t/τ))

  
• How does the charging equation for current compare to the discharging equation?

  They are the same in form
• What is the significance of Q₀ and V₀ in charging equations?

  They represent maximum values when fully charged
• How do you rearrange equations involving natural logs and exponential functions?

  Practice with ln and e functions
• What are the key equations for capacitor discharge and charge?

  • Discharge: I = I₀ e^(-t/τ)
  • Charge: Q = Q₀ (1 - e^(-t/τ))
  • Potential Difference (Discharge): V = V₀ e^(-t/τ)
  • Potential Difference (Charge): V = V₀ (1 - e^(-t/τ))

  
• What are the characteristics of exponential decay in capacitors?

  • Current, charge, and potential difference decrease exponentially
  • Time constant τ affects the rate of decay
  • Initial values influence the discharge duration

  
• What are the implications of the time constant τ in capacitor circuits?

  • τ = R × C determines discharge/charge rates
  • Smaller τ results in faster decay
  • Larger initial current leads to longer discharge time