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

Alternating Voltages and Currents

Physics

31. Alternating Current

Alternating Voltages and Currents

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Multiple Choice

An AC emf source is given by $ε = (170 V) \cos {2 π (60 Hz) t}$ . What is the instantaneous emf of this source at $t = 97 ms$ ?

30 V

45 V

130 V

170 V

210 V

72 V

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Verified step by step guidance

Start by identifying the given AC emf equation: ε = (170⁢V)⁢cos{2π(60⁢Hz)t}. This represents the instantaneous emf as a function of time.

Recognize that the equation is in the form ε = ε₀ cos(ωt), where ε₀ is the peak emf (170 V), and ω is the angular frequency. The angular frequency ω is given by ω = 2πf, where f is the frequency (60 Hz).

Substitute the given time t = 97 ms into the equation. First, convert 97 ms to seconds: t = 97 ms = 0.097 s.

Calculate the argument of the cosine function: ωt = 2π(60⁢Hz)(0.097⁢s). This will give you the angle in radians that you need to evaluate the cosine function.

Evaluate the cosine function at the calculated angle and multiply by the peak emf (170 V) to find the instantaneous emf at t = 97 ms. This will give you the value of the emf at that specific time.