Capacitors

• What is capacitance (C) defined as?

  Charge stored (Q) per unit potential difference (V)
• How is capacitance (C) mathematically expressed?

  C = $\frac{Q}{V}$
• What is a capacitor?

  An electrical component that stores charge
• What are the components of a parallel plate capacitor?

  Two conducting parallel plates with a gap

  
• What is the role of a dielectric in a capacitor?

  It separates the plates and affects capacitance

  
• What happens when a capacitor is connected to a power source?

  Opposite charges build up on the plates
• What is permittivity (ε) in relation to dielectrics?

  It measures the ability to store an electric field
• How is relative permittivity (εr) calculated?

  Ratio of dielectric permittivity to free space permittivity
• What is the formula for capacitance (C) in terms of area (A), distance (d), and relative permittivity (εr)?

  C = $\frac{A \cdot \varepsilon_r \cdot \varepsilon_0}{d}$
• What are polar molecules in a dielectric?

  Molecules with positive and negative ends
• How do polar molecules behave in an electric field?

  They align themselves with the field
• What effect do polar molecules have on the electric field of a capacitor?

  They oppose the field, reducing its strength
• How does capacitance change when the electric field strength decreases?

  Capacitance increases as potential difference decreases
• What is the formula for energy (E) stored in a capacitor?

  E = $\frac{1}{2} QV$
• What shape does the graph of charge (Q) against potential difference (V) take?

  A straight line through the origin

  
• How can you derive variations of the energy stored formula?

  By substituting capacitance into the energy formula
• What is the time constant for a capacitor charging graph?

  Approximately 2.5 seconds
• How do you find the time taken for voltage to halve?

  Using the formula $T_{1/2} =$$0.69RC$
• What is the time taken for voltage to halve with a 600 nF capacitor and 100 kΩ resistor?

  0.0414 seconds
• How do you find the charge after a certain time for a discharging capacitor?

  Using the formula $Q =$$Q_0 e^{-\frac{t}{RC}}$
• What is the charge after 5 seconds for a 300 μF capacitor with 5 C initial charge?

  4.8 C
• How can you calculate the time constant from graphs?

  By finding values at 0.37 or 0.63 of initial value
• What is the time constant (RC) in relation to capacitor discharge?

  Time taken to discharge to 0.37 of initial value
• What happens to current, charge, and potential difference during capacitor discharge?

  They all fall exponentially
• What is the formula for current during capacitor discharge?

  I = $I_0 e^{-\frac{t}{RC}}$
• What is the formula for potential difference during capacitor discharge?

  V = $V_0 e^{-\frac{t}{RC}}$
• What is the formula for charge during capacitor discharge?

  Q = $Q_0 e^{-\frac{t}{RC}}$
• What is the product of resistance and capacitance (RC) known as?

  The time constant
• What does the time constant indicate in capacitor charging and discharging?

  Time taken to reach specific fractions of initial value
• What are the steps to charge a capacitor in a circuit?

  • Connect to a power supply and resistor
  • Measure potential difference and current
  • Plot graphs of voltage and current against time
  • Calculate charge using $Q =$$I \times t$
• What are the steps to discharge a capacitor through a resistor?

  • Connect to a closed circuit with a resistor
  • Measure voltage and current
  • Plot graphs of voltage, current, and charge against time
• What are the key characteristics of capacitor charging and discharging graphs?

  • Exponential curves for charge, voltage, and current
  • Current decreases as charge builds up
  • Voltage increases until it reaches maximum
  • Charge decreases exponentially during discharge