Table of contents

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

Phasors for Resistors

Physics

31. Alternating Current

Phasors for Resistors

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Multiple Choice

A 12 Ω resistor is connected to an AC source. If the resistor's voltage phasor is initially at 0° , and the figure below shows the phasor after 0.04 s, answer the following:
a) What is the angular frequency of the source? Assume the phasor is on its first rotation.
b) What does the current phasor diagram look like?
c) What is the current in the circuit at this point (t = 0.04 ?)?

a) ω = 0.029 s^-1 b) θ = 132^o c) -0.31A

a) ω = 0.029 s^-1 b) θ = 132^o c) 0.31A

a) ω = 18.3 s^-1 b) θ = 42^o c) 0.31A

a) ω = 18.3 s^-1 b) θ = 42^o c) 0.42A

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Verified step by step guidance

To find the angular frequency (ω), we need to use the relationship between the angular displacement (θ) and time (t). The angular displacement is given as 42° which needs to be converted to radians. Use the formula: θ (radians) = θ (degrees) × (π/180).

The angular frequency (ω) is defined as the rate of change of the angular displacement with respect to time. Use the formula: ω = θ / t, where θ is in radians and t is the time interval (0.04 s).

For the current phasor diagram, note that in a purely resistive circuit, the current and voltage are in phase. Therefore, the current phasor will also be at 42° at t = 0.04 s.

To find the current in the circuit, use Ohm's Law for AC circuits: I = V/R, where V is the voltage across the resistor (5 V as shown in the phasor diagram) and R is the resistance (12 Ω).

Calculate the current using the formula: I = 5 V / 12 Ω. The current will be in phase with the voltage, so it will have the same angle of 42° at t = 0.04 s.