Will a frequency f = 60 Hz or ω = 75 s −1 produce a larger max current in an inductor connected to an AC source?

Alright guys. I hope you're able to solve this problem on your own. If not, here's a little bit of help. Will a frequency f equals 60 hertz or omega equals 75 inverse seconds produce a larger max current in an inductor connected to an AC source? Which of these currents will produce a larger maximum current? So remember that the maximum current in an inductor is just the voltage across, the maximum voltage across the source. Okay remember that this is supposed to be the maximum voltage across the inductor but because the inductor is connected directly to the source, they share the maximum voltage. That's just Kirchhoff's loop rule. Divided by the inductive capacitance. Sorry, the inductive reactants. Now, the inductive reactants depends upon the angular frequency. So whichever of these two frequencies has a larger angular frequency is going to produce a larger inductive reactance which is going to produce a smaller current. So larger, omega, smaller, current. Okay? So be very careful. This is a linear frequency. This is an angular frequency. We need to convert the linear frequency into an angular frequency. So we'll say that the angular frequency 1 is 2pif1 is 2pi times 60 which is 377 inverse seconds and we'll say that omega2 which is already given as an angular frequency is 75 inverse seconds. Okay so 75 is bigger than 60 but you have to remember that they both to be expressed as angular frequencies. So the larger one leads to a smaller current so the smaller frequency leads to a larger current. This is the smaller angular frequency, so this leads to the largest maximum current. Alright guys, thanks for watching.

Table of contents

Skip topic navigation

0. Math Review31m
- Math Review
  31m
1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
3. Vectors2h 43m
4. 2D Kinematics1h 42m
5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
7. Friction, Inclines, Systems2h 44m
8. Centripetal Forces & Gravitation7h 26m
9. Work & Energy1h 59m
10. Conservation of Energy2h 54m
11. Momentum & Impulse3h 40m
12. Rotational Kinematics2h 59m
13. Rotational Inertia & Energy7h 4m
14. Torque & Rotational Dynamics2h 5m
15. Rotational Equilibrium3h 39m
16. Angular Momentum3h 6m
17. Periodic Motion2h 9m
18. Waves & Sound3h 40m
19. Fluid Mechanics4h 27m
20. Heat and Temperature3h 7m
21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
23. The Second Law of Thermodynamics3h 11m
24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
29. Sources of Magnetic Field2h 30m
30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

31. Alternating Current

Inductors in AC Circuits

Physics

31. Alternating Current

Inductors in AC Circuits

Previous problemNext problem

Struggling with Physics?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

Will a frequency f = 60 Hz or ω = 75 s⁻¹ produce a larger max current in an inductor connected to an AC source?

f = 60 Hz

ω = 75 s^-1

Both produce the same amount of maximum current

More information is required.

Previous problemNext problem

Verified step by step guidance

Understand that the maximum current in an inductor connected to an AC source is determined by the inductive reactance, which is given by the formula: \( X_L = \omega L \), where \( \omega \) is the angular frequency and \( L \) is the inductance.

Recall the relationship between frequency \( f \) and angular frequency \( \omega \), which is \( \omega = 2\pi f \). This allows us to convert between the two if needed.

Calculate the inductive reactance for both given frequencies. For \( f = 60 \text{ Hz} \), first convert to angular frequency using \( \omega = 2\pi \times 60 \). Then, use \( X_L = \omega L \) to find the reactance.

For \( \omega = 75 \text{ s}^{-1} \), directly use the given angular frequency in the formula \( X_L = \omega L \) to find the reactance.

Compare the inductive reactance values from both scenarios. The scenario with the lower reactance will allow a larger maximum current, as current \( I \) is inversely proportional to reactance \( X_L \) in the formula \( I = \frac{V}{X_L} \), where \( V \) is the voltage of the AC source.