Chapter 32: Q. 2 (page 923)

The emf phasor in FIGURE EX32.2 is shown at $t = 15 m s$ .
a. What is the angular frequency $ω$ ? Assume this is the first rotation.
b. What is the instantaneous value of the emf?

Short Answer

Expert verified

The angular frequency $ω$ is $244 r a d / s$ and instantaneous value of the emf is $- 10 V$ .

Step by step solution

Part (a) Step 1: Given information

We are given that time $t = 15 m s$ , $E_{o} = 12 V$ and $\emptyset = 150^{\circ}$ (as the phasor rotates anticlockwise towards X-axis)

Part (a) Step 2: Calculation

As we know that-

E = E_{0} \cos (ω t + \emptyset)

$ω t = 180^{\circ} + \emptyset ω t = 180^{\circ} + 30^{\circ} ω t = 210^{\circ}$ (as phasor rotates anticlockwise)

Now converting degrees into radian

$210^{\circ} = 210^{\circ} \frac{πrad}{180^{\circ}} = \frac{7 πrad}{6}$

Now,

$ω t = \frac{7 πrad}{6} ω (15 \times 10^{- 3}) = \frac{7 πrad}{6} ω = 244 r a d / s$

Part (b) Step 1: Given information

We are given that-

$E_{0} = 12 V \emptyset = 150^{\circ}$

Part (b) Step 2: Calculation

As we know that peak value $E_{0} = 12 V$ will occur when $ω t = 0$

So now in the expression,

$E = E_{0} \cos (ω t + \emptyset) E = 12 V \cos (0 + 150^{\circ}) E = - 10 V$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

The emf phasor in FIGURE EX32.2 is shown at $t = 15 m s$ .
a. What is the angular frequency $ω$ ? Assume this is the first rotation.
b. What is the instantaneous value of the emf?

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Calculation

Part (b) Step 1: Given information

Part (b) Step 2: Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Energy Physics

Electricity and Magnetism

Measurements

Particle Model of Matter

Geometrical and Physical Optics

Circular Motion and Gravitation

Study anywhere. Anytime. Across all devices.

The emf phasor in FIGURE EX32.2 is shown at t=15ms.a. What is the angular frequency ω? Assume this is the first rotation.b. What is the instantaneous value of the emf?

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Calculation

Part (b) Step 1: Given information

Part (b) Step 2: Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Energy Physics

Electricity and Magnetism

Measurements

Particle Model of Matter

Geometrical and Physical Optics

Circular Motion and Gravitation

Study anywhere. Anytime. Across all devices.

The emf phasor in FIGURE EX32.2 is shown at $t = 15 m s$ .
a. What is the angular frequency $ω$ ? Assume this is the first rotation.
b. What is the instantaneous value of the emf?