A Eletricidade na Engenharia

Chapter 13

1. a.   10 V

1. 15 ms: −10 V, 20 ms: 0 V

1. 20 V
2. 20 ms
3. 2 cycles

1. a.   200 μA

1. 1 μs: 200 μA, 7 μs: −200 µA

1. 400 μA
2. 4 μs

1. 2.5 cycles

1. a.   40 mV

1. 1.5 ms: −40 mV, 5:1 ms:  40 mV

1. 80 mV
2. 2 ms
3. 3.5 cycles

4.

a.

T =

1

1

= 5 ms

f

200 Hz

b.

T =

1

1

= 25 ns

f

40 MHz

c.

T =

1

1

= 50 μs

f

20 kHz

d.

T =

1

=

1

= 1 s

1 Hz

f

5.

a.

f =

1

1

= 1 Hz

T

1s

b.

f =

1

1

= 16 Hz

1

T

s

16

c.

f =

1

=

1

= 25 Hz

T

40 ms

d.

f =

1

=

1

= 40 kHz

T

25 μs

6.

T =

1

= 1 ms, 5(1 ms) = 5 ms

1 kHz

7.

T =

24 ms

= 0.3 ms

80 cycles

156        CHAPTER 13

1. f = 42 cycles = 7 Hz 6 s

1. a. Vpeak = (2.5 div.)(50 mV/div) = 125 mV b. T = (3.2 div.)(10 μs/div.) = 32 μs

[pic 1]

1

1

= 31.25 kHz

c.

f = T

32  s

10.

a.

Radians =

40  = 0.22 π rad

180

⎛

π

⎞

π

b.

Radians = ⎜

⎟60° =

rad

⎝

180° ⎠

3

= 0.75π rad

c.

Radians =

135

180

⎛

π

⎞

= 0.94π rad

d.

Radians = ⎜

⎟170°

⎝

180° ⎠

180

= 60°

11.

a.

Degrees =

3

180

b.

Degrees =

1.2  = 216°

⎛

180° ⎞

1

π =18°

c.

Degrees = ⎜

⎟

π

10

⎝

⎠

⎛180° ⎞

d.

Degrees = ⎜

⎟ 0.6 π = 108°

π

⎝

⎠

12.

a.

ω =

2

2

= 3.49 rad/s

T

1.8 s

b.

ω =

2π

= 20.94 × 103 rad/s

0.3 ×10−3 s

c.

ω =

2

= 785.4 × 103 rad/s

10 6  s

8

d.

ω =

2

= 1.57 × 106 rad/s

4

10 6 s

1. a.   ω = 2π f = 2π (100 Hz) = 628.32 rad/s

1. ω = 2π f = 2π (0.25 kHz) = 1.57 × 103 rad/s
2. ω = 2π f = 2π (2 kHz) = 12.56 × 103 rad/s

1. ω = 2π f = 2π (0.004 MHz) = 25.13 × 103 rad/s

CHAPTER 13        157

14.

a.

ω = 2π f =

2π

⇒ f =

ω

2π

T

T =

2π

=

1

ω

f

f =

ω

=

754 rad/s

= 120 Hz, T = 8.33 ms

2π

2π

b.

f =

12 rad/s

= 1.91 Hz, T = 523.6 ms

2

2

c.

f =

ω

=

6000 rad/s

= 954.93 Hz, T = 1.05 ms

2π

2π

0.16 rad/s

= 25.46 ×

−3

d.

f =

10

Hz, T = 39.28 ms

2

2

15.

(60°)

radians

3

180

t =

/ 3 rad

/ 3 rad

1

1

= 2.78 ms

(6)(60)

360

2  f

2  (60 Hz)

⎛

π

⎞

π

, α = ωt

⇒ ω =

α

π

/ 6

16.

(30°) ⎜

⎟

=

=

= 104.7 rad/s

5 ×10−3

⎝180° ⎠

6

t

s

17.

a.

Amplitude = 20, f =

ω

=

377 rad/s

= 60 Hz

2π

2π

1. Amplitude = 12, f = 120 Hz

c.

Amplitude = 106, f =

ω

=

10,000 rad/s

= 1591.55 Hz

2π

2π

d.

Amplitude = 8, f =

10,058 rad/s

= 1.6 kHz

2

2

18.

−

19.

−

20.

T =

2π

=

2π

= 40 ms,

1

cycle = 20 ms

ω

157

2

1. i = 0.5 sin 72° = 0.5(0.9511) = 0.48 A

	1.2π	⎛	180° ⎞	= 216°
22.	⎝⎜			⎠⎟
	π

• = 20 sin 216° = 20(−0.588) = −11.76 V

158        CHAPTER 13

1. 6 × 10−3 = 30 × 10−3 sin α 0.2 = sin α

• = sin−1 0.2 = 11.54° and 180° −

1. υ = Vm sin α

40 = Vm sin 30° = Vm (0.5)

∴Vm = 40 = 80 V

0.5

[pic 2]

and υ = 80 sin 523.58t

1. −

1. −

1. a.   υ = 6 × 10 3 sin (2π 2000t + 30°)

---

11.54° = 168.46°

30° = 1 ms

[pic 3][pic 4]

360°        T

⎛360⎞

T = 1 ms ⎜        ⎟ = 12 ms

[pic 5]

⎝30⎠

f =	1	=		1	= 83.33 Hz
	12 ×10−3 s
	T

ω = 2π f = (2π)(83.33 Hz) = 523.58 rad/s

b.   i = 20 × 10−3 sin(2π 60t − 60°)

...