Capacitors

• What is the symbol for a capacitor?


  Two parallel lines
• What is the primary function of a capacitor?


  To store electrical charge
• How is the amount of charge stored on a capacitor related to the potential difference?


  The amount of charge is proportional to the potential difference
• What is the formula for capacitance?

  Capacitance \( C = \frac{Q}{V} \)
• What does capacitance measure?


  It measures the amount of charge stored per unit of potential difference
• What is the unit of capacitance?


  Farad
• How is one farad defined?


  One farad is the capacitance when one coulomb of charge is stored for one volt
• Describe the flow of electrons when a capacitor is charging.


  Electrons flow from the negative terminal of the cell to the negative plate of the capacitor
• What happens to the charges on the plates of a capacitor during charging?


  The plates acquire equal and opposite charges
• How can a charged capacitor be used in a circuit?


  It can be connected to a light bulb to provide power
• What is the rule for adding capacitors in parallel?


  • Total capacitance \( C_{\text{total}} = C_1 + C_2 \)
  • The total capacitance is the algebraic sum of the individual capacitances
• If two capacitors of 300 microfarads are connected in parallel, what is the total capacitance?


  600 microfarads
• What is the rule for adding capacitors in series?


  • Total capacitance \( \frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} \)
  • The reciprocal of the total capacitance is the sum of the reciprocals of the individual capacitances
• What is the total capacitance of two capacitors of 300 microfarads connected in series?


  150 microfarads
• Why is the rule for adding capacitors in series opposite to that of resistors?


  Because in series, the charge is the same while the voltage is shared
• What happens to voltage and charge in a parallel circuit with capacitors?


  • Voltage is the same across all capacitors
  • Total charge \( Q_{\text{total}} = Q_1 + Q_2 \)
• What happens to voltage and charge in a series circuit with capacitors?


  • Current is the same through all capacitors
  • Total charge \( Q_{\text{total}} = Q_1 = Q_2 \)
• What does Kirchhoff's second law state regarding potential difference in a series circuit?


  The sum of the EMFs equals the sum of the potential differences across each component
• How does the voltage across a discharging capacitor change over time?


  It decreases exponentially
• What is the equation for the voltage across a discharging capacitor at time \( t \)?


  \( V = V_0 e^{-\frac{t}{CR}} \)
• If a 500 microfarad capacitor is charged to 6 volts and discharged through a 500 kilo-ohm resistor, what is the voltage across the capacitor after 150 seconds?


  1. 29 volts
• What characterizes an exponential function in terms of decay?


  • The ratio of values decreases by the same factor in equal time intervals
  • For example, if \( V_1 \) decreases to \( V_2 \), then \( V_2 \) decreases to \( V_3 \) by the same factor
• How can you rearrange the equation for time \( t \) in terms of voltage across a capacitor?


  \( t = CR \ln\left(\frac{V_0}{V}\right) \)
• What is the time constant in relation to capacitance and resistance?


  • The time constant \( \tau = CR \)
  • It determines the charging and discharging time of a capacitor
• What are the units of the time constant \( \tau \)?


  Seconds
• What happens to the potential difference at the time equal to the time constant?


  The potential difference drops to 37% of its original value
• How can the time constant be determined from a graph?


  • The time constant is the time it takes for the voltage to drop to 37% of its initial value
  • This can be observed in graphs of voltage, current, or charge against time
• What is the relationship between the voltage across a charging capacitor and the voltage across a resistor in the circuit?


  The voltage across the capacitor increases while the voltage across the resistor decreases exponentially
• What is the equation for the voltage across the resistor in a charging capacitor circuit?


  \( V_R = V_0 e^{-\frac{t}{CR}} \)
• How can the potential difference across a charging capacitor be expressed in terms of the initial voltage?


  \( V_C = V_0 \left(1 - e^{-\frac{t}{CR}}\right) \)
• How does the charge across a capacitor change during charging?


  \( Q_C = Q_0 \left(1 - e^{-\frac{t}{CR}}\right) \)
• How does the current in a charging circuit behave over time?


  The current decreases as the capacitor charges
• What happens to the current when the capacitor reaches maximum potential difference?


  The current drops to zero