Inductance - AP Physics C Electricity and Magnetism

1. Which type of inductance involves two electrical circuits?

   Mutual inductance. Coupling between separate coils or circuits.

2. Identify the symbol commonly used for inductance in equations.

   $L$. Standard notation in electromagnetic equations.

3. How does a change in current affect the induced emf in an inductor?

   Emf is proportional to rate of change. Faster current changes produce larger opposing EMF.

4. What is the symbol for mutual inductance in equations?

   $M$. Standard symbol for mutual inductance coefficient.

5. State the formula for self-induced emf.

   $\text{emf} = -L \frac{dI}{dt}$. Negative sign shows opposition to current change (Lenz's law).

6. Calculate the emf induced if L=2 H and $\frac{dI}{dt}=3 A/s$.

   $\text{emf} = -6 \text{ V}$. From $\text{emf} = -L \frac{dI}{dt} = -2 \times 3$.

7. What is the effect of decreasing the number of turns on a coil's inductance?

   Decreases inductance. Fewer turns reduce magnetic flux linkage proportionally.

8. What happens to inductance if the coil length is halved?

   Inductance doubles. Length appears in denominator, so halving doubles inductance.

9. Calculate the energy stored in an inductor with L=0.5 H and I=4 A.

   $E = 4 \text{ J}$. Using $E = \frac{1}{2} \times 0.5 \times 4^2 = 4$ J.

10. State the formula for inductance of a solenoid.

    $L = \frac{\text{N}^2 \times \text{A} \times \text{μ}}{\text{l}}$. Relates turns squared, area, and permeability to length.

11. What is mutual inductance?

    Induction between two coils. Current in one coil induces flux in another coil.

12. What is the relationship between inductance and magnetic flux?

    $L = \frac{\text{N} \times \text{Φ}}{\text{I}}$. Inductance equals flux linkage divided by current.

13. What is the induced emf when L=0.1 H and the current change is 10 A/s?

    $\text{emf} = -1 \text{ V}$. Using $\text{emf} = -L \frac{dI}{dt} = -0.1 \times 10$.

14. What is the role of permeability in inductance?

    Higher permeability increases inductance. Higher permeability strengthens magnetic field in core.

15. How does inductance relate to back EMF in a circuit?

    Inductance opposes change in current. Creates opposing voltage when current changes (Lenz's law).

16. Describe the effect of core saturation on inductance.

    Reduces inductance. Saturated core cannot increase flux despite more current.

17. What is the inductance of a coil with back emf of 12 V and $\frac{dI}{dt} = 4 A/s$?

    $L = 3 \text{ H}$. From $L = \frac{\text{emf}}{dI/dt} = \frac{12}{4}$.

18. Which formula represents the energy stored in a magnetic field of an inductor?

    $E = \frac{1}{2} \times L \times I^2$. Standard formula for magnetic energy storage in inductors.

19. State the unit of mutual inductance.

    Henry (H). Same unit as self-inductance, both measure flux-current ratio.

20. State the energy stored in an inductor formula.

    $E = \frac{1}{2} \times L \times I^2$. Energy proportional to inductance and current squared.

21. Identify the factor that does not affect inductance.

    Temperature. Inductance depends on physical geometry, not thermal properties.

22. What does the negative sign in $-\frac{dI}{dt}$ indicate in Faraday's Law?

    Direction opposes change. Indicates EMF opposes the current change (Lenz's law).

23. Which physical quantity opposes changes in current in an inductor?

    Induced EMF. Back EMF opposes changes per Lenz's law.

24. What effect does tightly winding a coil have on its inductance?

    Increases inductance. Tighter winding increases turns per unit length.

25. State the formula for mutual inductance.

    $M = \frac{\text{N}_2 \times \text{Φ}_{21}}{\text{I}_1}$. Flux through coil 2 divided by current in coil 1.

26. What type of inductance occurs in a single circuit?

    Self-inductance. Single coil inducing EMF in itself.

27. What is self-inductance?

    Induction in a single coil. Coil induces EMF in itself when current changes.

28. What is the effect of increasing current on the energy stored in an inductor?

    Increases stored energy. Energy depends on current squared, so increases rapidly.

29. What is the effect of a core material with higher permeability?

    Increases inductance. Higher permeability concentrates magnetic field lines better.

30. How does increasing the number of turns in a coil affect its inductance?

    Increases inductance. More turns create stronger magnetic field and flux linkage.

31. How is inductance related to coil area?

    Larger area increases inductance. Larger area captures more magnetic flux lines.

32. State the proportional relationship between inductance and coil length.

    Inversely proportional. Length in denominator creates inverse relationship.

33. What is the induced emf when $L=0.1 \text{ H}$ and the current change is $10 \text{ A/s}$?

    $\text{emf} = -1 \text{ V}$. Using $\text{emf} = -L \frac{dI}{dt} = -0.1 \times 10$.

34. Calculate the energy if L=0.8 H and I=5 A.

    $E = 10 \text{ J}$. Using $E = \frac{1}{2} \times 0.8 \times 5^2 = 10$ J.

35. What is the inductance of a coil if the self-induced emf is 5V and $\frac{dI}{dt} = 2 A/s$?

    $L = 2.5 \text{ H}$. From $\text{emf} = L \frac{dI}{dt}$, so $L = \frac{5}{2}$.

36. What is the SI unit of inductance?

    Henry (H). Named after Joseph Henry who discovered electromagnetic induction.

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