Conservation of Electric Energy - AP Physics C Electricity and Magnetism

1. State the formula for energy stored in a magnetic field.

   $U = \frac{1}{2}LI^2$. Energy stored in magnetic field of inductor.

2. State the formula for electric potential in terms of work done.

   $V = \frac{W}{q}$. Potential is work per unit charge.

3. Calculate power consumed by a $5 \text{ A}$ current through $10 \text{ V}$.

   $50 \text{ W}$. Power equals current times voltage: $5 \times 10$.

4. State the energy conservation law in electrical circuits.

   Energy supplied = Energy consumed + Energy stored. Fundamental energy balance in electrical systems.

5. State the equation for energy stored in a dielectric medium.

   $U = \frac{1}{2} \text{ε} E^2 A d$. Energy in dielectric includes permittivity $\varepsilon$.

6. State the formula for the energy of a moving charge in an electric field.

   $U = qEd$. Energy of charge moving through electric field.

7. State the energy conservation equation for electric circuits.

   $\text{Energy input} = \text{Energy output}$. Fundamental principle of energy conservation.

8. State the energy conservation equation for an LC circuit.

   $\frac{1}{2}CV^2 + \frac{1}{2}LI^2 = \text{constant}$. Energy oscillates between electric and magnetic forms.

9. Identify the relationship between electric field and energy density.

   $u = \frac{1}{2} \text{ε}_0 E^2$. Energy density proportional to field squared.

10. What quantity is conserved in an electrostatic process?

    Electric energy. Conserved quantity in electrostatic interactions.

11. State the formula for power in terms of resistance and current.

    $P = I^2R$. Power dissipated through resistance.

12. Identify the electric energy formula for charge $q$ and potential $V$.

    $U = qV$. Basic formula for electric potential energy.

13. Find the potential energy change for $q = 2 \text{ C}$ moving from $3 \text{ V}$ to $5 \text{ V}$.

    $4 \text{ J}$. Change equals charge times voltage difference: $2(5-3)$.

14. What is the formula for energy stored in terms of charge and capacitance?

    $U = \frac{q^2}{2C}$. Alternative form using charge and capacitance.

15. State the formula for electric potential energy.

    $U = qV$. Energy equals charge times electric potential.

16. Calculate the work done moving $3 \text{ C}$ through $10 \text{ V}$.

    $30 \text{ J}$. Work equals charge times potential difference: $3 \times 10$.

17. Which formula calculates power using voltage and resistance?

    $P = \frac{V^2}{R}$. Power using voltage and resistance relationship.

18. Calculate power for $V=12 \text{V}$ and $R=6 \text{Ω}$.

    $24 \text{W}$. Power equals $\frac{V^2}{R} = \frac{144}{6}$.

19. Calculate energy stored in an inductor with $L=2 \text{ H}$ and $I=3 \text{ A}$.

    $9 \text{ J}$. Using $U = \frac{1}{2}LI^2 = \frac{1}{2}(2)(3)^2$.

20. What is the unit of electric field energy density?

    Joules per cubic meter (J/m³). Energy density has units of energy per volume.

21. Calculate the energy loss for $R=5 \text{ Ω}$ and $I=3 \text{ A}$ over $2 \text{ s}$.

    $90 \text{ J}$. Energy equals $I^2 R t = 9(5)(2)$.

22. What is the formula for electric energy loss in a resistor?

    $P = I^2R$. Power dissipated as heat in resistor.

23. What is the formula for energy stored in a capacitor?

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

24. Calculate work done on $q=5 \text{ C}$ in field $E=10 \text{ N/C}$ over $3 \text{ m}$.

    $150 \text{ J}$. Work equals $qEd = 5(10)(3)$.

25. What is the principle of conservation of electric energy?

    Total electric energy is constant in a closed system. Energy cannot be created or destroyed in electric systems.

26. Identify the expression for electric energy in terms of field and volume.

    $U = \frac{1}{2} \text{ε}_0 E^2 V$. Energy density times volume gives total energy.

27. What is the unit of electric potential difference?

    Volt (V). Standard unit for electric potential.

28. State the formula for energy stored in an electric field.

    $U = \frac{1}{2} \text{ε}_0 E^2 A d$. Total energy stored in uniform electric field.

29. Identify the formula for energy transfer in an electric field.

    $W = qEd$. Work done moving charge through electric field.

30. What is the relationship between capacitance, charge, and voltage?

    $C = \frac{q}{V}$. Defines capacitance as charge per voltage.

31. What is the unit of electric potential energy?

    Joule (J). Same unit as mechanical energy.

32. Calculate the energy stored in a $10 \text{ F}$ capacitor with $5 \text{ V}$ potential.

    $125 \text{ J}$. Using $U = \frac{1}{2}CV^2 = \frac{1}{2}(10)(5)^2$.

33. What is the formula for power in terms of current and voltage?

    $P = IV$. Power is rate of energy transfer.

34. Identify the formula relating electric field and potential difference.

    $E = -\frac{dV}{dx}$. Electric field is negative gradient of potential.

35. Calculate power for $V=12 \text{ V}$ and $R=6 \text{ Ω}$.

    $24 \text{ W}$. Power equals $\frac{V^2}{R} = \frac{144}{6}$.

36. What is the energy formula in terms of voltage and capacitance?

    $U = \frac{1}{2}CV^2$. Standard capacitor energy formula.

37. What happens to electric energy in a closed system?

    It remains constant. Conservation law for isolated electric systems.

38. Calculate the energy stored for $q = 4 \text{ C}$ and $C = 8 \text{ F}$.

    $1 \text{ J}$. Using $U = \frac{q^2}{2C} = \frac{16}{16}$.

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