Capacitors - AP Physics C Electricity and Magnetism

1. State the equation for voltage across a charging capacitor over time.

   $V(t) = V_0(1 - e^{-t/RC})$. Exponential approach to final voltage with time constant $RC$.

2. What effect does a dielectric have on capacitance?

   Increases capacitance. Dielectric constant $k > 1$ multiplies the capacitance.

3. What does the time constant $\tau$ signify in an RC circuit?

   Time to reach $63\%$ of final value. Characteristic time for exponential charging or discharging process.

4. What is the effect of connecting capacitors in parallel?

   Increases equivalent capacitance. Parallel connection sums individual capacitances.

5. Identify the formula for the electric field in a capacitor.

   $E = \frac{V}{d}$. Electric field equals voltage divided by plate separation.

6. State the formula for equivalent capacitance in parallel.

   $C_{\text{eq}} = C_1 + C_2 + \dots$. Parallel capacitors combine by direct addition of values.

7. What is the effect of reducing the distance between capacitor plates?

   Increases capacitance. From $C = \frac{\varepsilon A}{d}$, smaller $d$ increases capacitance.

8. State the formula for equivalent capacitance in series.

   $\frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} + \dots$. Series capacitors combine like parallel resistors with reciprocal addition.

9. How does a dielectric affect the electric field in a capacitor?

   Decreases the electric field. Dielectric reduces field by factor of dielectric constant $k$.

10. How does distance between plates affect capacitance?

    Capacitance decreases with increased distance. From $C = \frac{\varepsilon A}{d}$, capacitance is inversely proportional to distance.

11. How does a dielectric affect capacitance mathematically?

    $C' = kC$. Dielectric constant $k$ multiplies the original capacitance value.

12. What happens to capacitance if the plate area increases?

    Capacitance increases. From $C = \frac{\varepsilon A}{d}$, capacitance is directly proportional to area.

13. What factor does the dielectric constant affect?

    Capacitance. Dielectric constant directly multiplies the capacitance value.

14. What is the energy density in a capacitor?

    $u = \frac{1}{2}\varepsilon E^2$. Energy density depends on permittivity and electric field squared.

15. State the relationship between energy, capacitance, and voltage.

    $U = \frac{1}{2}CV^2$. Energy stored is half the product of capacitance and voltage squared.

16. What is the initial current in a charging capacitor circuit?

    $I_0 = \frac{V}{R}$. Initial current follows Ohm's law before capacitor charges.

17. State the formula for the potential difference across a capacitor.

    $V = \frac{Q}{C}$. Voltage equals charge divided by capacitance.

18. What is the relationship between energy density and electric field?

    $u = \frac{1}{2}\varepsilon E^2$. Energy density is proportional to permittivity and field squared.

19. Identify the formula for energy stored in terms of charge.

    $U = \frac{1}{2} \frac{Q^2}{C}$. Alternative energy formula using charge instead of voltage.

20. Define the time constant for an RC circuit.

    $\tau = RC$. Product of resistance and capacitance determines charging rate.

21. What happens to stored energy if capacitance doubles?

    Stored energy doubles. From $U = \frac{1}{2}CV^2$, energy is directly proportional to capacitance.

22. What is the effect of connecting capacitors in series?

    Decreases equivalent capacitance. Series connection reduces total capacitance below smallest value.

23. State the formula for the capacitance of a parallel plate capacitor.

    $C = \frac{\varepsilon A}{d}$. Capacitance depends on area $A$, distance $d$, and permittivity $\varepsilon$.

24. What is the initial voltage across a capacitor at $t = 0$ in a DC circuit?

    Zero volts. Uncharged capacitor acts as short circuit initially.

25. What is the role of a capacitor in a circuit?

    Stores electrical energy. Capacitors accumulate charge and release it when needed.

26. State the formula for capacitors in parallel.

    $C_{\text{eq}} = C_1 + C_2 + \dots$. Parallel capacitors add directly like series resistors.

27. How does adding a dielectric change the capacitance?

    Increases capacitance. Dielectric material increases capacitance by factor $k$.

28. What is the dielectric breakdown?

    Failure of dielectric under high voltage. Electric field exceeds dielectric strength, causing material failure.

29. What is the equation for voltage across a discharging capacitor?

    $V(t) = V_0 e^{-t/RC}$. Exponential decay from initial voltage with time constant $RC$.

30. What is the unit of capacitance?

    Farad (F). Named after Michael Faraday, represents charge per unit voltage.

31. What is the relationship between charge and voltage in a capacitor?

    $Q = CV$. Charge is proportional to both capacitance and voltage.

32. What does the symbol $\varepsilon_0$ represent?

    Permittivity of free space. Fundamental constant relating electric field to electric displacement.

33. What is the effect of inserting a dielectric with $k > 1$?

    Increases capacitance. Any dielectric with $k > 1$ increases the original capacitance.

34. What is the formula for work done to charge a capacitor?

    $W = \frac{1}{2}CV^2$. Work equals energy stored in the electric field.

35. State the formula for capacitors in series.

    $\frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} + \dots$. Series capacitors add reciprocally like parallel resistors.

36. Identify the energy stored in a capacitor formula.

    $U = \frac{1}{2}CV^2$. Energy is proportional to capacitance and voltage squared.

37. State the relationship between charge, voltage, and capacitance.

    $Q = CV$. Fundamental relationship defining capacitance as charge per voltage.

38. What is the formula for the maximum charge a capacitor can hold?

    $Q = CV$. Maximum charge depends on capacitance and applied voltage.

39. Identify the expression for the electric displacement field $D$.

    $D = \varepsilon E$. Displacement field relates permittivity to electric field strength.

40. Identify the formula for charge on a capacitor in a DC circuit.

    $Q = CV$. Fundamental relationship between charge, capacitance, and voltage.

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