1 of 155

Capacitor

Circuits

2 of 155

+

-

12V

3 of 155

12 V

-

+

4 of 155

C₁

V

C₂

5 of 155

C₁=1 μF

10 V

C₂=2 μF

6 of 155

C₁=1 μF

V

C_eq=C₁+C₂=3 μF

V

C₂=2 μF

7 of 155

C₁=1 μF

V

C₂=2 μF

8 of 155

C₁=1 μF

12 V

C₃=3 μF

C₂=2 μF

9 of 155

12 V

C₁=6.0 μF

C₂=4.0 μF

C₃=1.0 μF

C₄=2.0 μF

C₅=2.0 μF

12 V

C₁=6.0 μF

C₂=6.0 μF

C₃=1.0 μF

C₄=1.0 μF

C₅=2.0 μF

10 of 155

12 V

C₁=1.0 μF

C₂=3.0 μF

C₃=1.0 μF

C₄=3.0 μF

C₅=3.0 μF

12 V

C₁=6.0 μF

C₂=4.0 μF

C₃=1.0 μF

C_4,5=4.0 μF

12 V

C₁=6.0 μF

C₂=4.0 μF

C₄=1.0 μF

C₃=4.0 μF

11 of 155

12 V

C₁=

3.0 μF

C₂=

3.0 μF

C₃=

6.0 μF

C₄=

6.0 μF

C₅=

4.0 μF

C₆=

4.0 μF

C₇=2.0 μF

	C_eq=
V₁=	Q₁=
V₂=	Q₂=
V₃=	Q₃=
V₄=	Q₄=
V₅=	Q₅=
V₆=	Q₆=
V₇=	Q₇=

12 of 155

12 V

C₁=

1.0 μF

C₂=

3.0 μF

C₃=

6.0 μF

C₄=

1.0 μF

C₅=

2.0 μF

C₆=

2.0 μF

C₇=1.0 μF

	C_eq=
V₁=	Q₁=
V₂=	Q₂=
V₃=	Q₃=
V₄=	Q₄=
V₅=	Q₅=
V₆=	Q₆=
V₇=	Q₇=

13 of 155

12 V

C₁=6.0 μF

C₂=4.0 μF

C₃=1.0 μF

C₄=2.0 μF

C₅=2.0 μF

14 of 155

12 V

C₁=2.0 μF

C₂=6.0 μF

C₃=1.0 μF

C₄=2.0 μF

C₄

=1.0 μF

15 of 155

C₁=2.0 μF

A

C₃=1.0 μF

C₄=2.0 μF

B

16 of 155

12 V

-

+

+Q

-Q

+Q

-Q

17 of 155

V

C₁=3 μF

C₂=6 μF

18 of 155

V

C₁=3 μF

C₂=6 μF

12 V

C₁=3 μF

C₂=6 μF

19 of 155

C₁=2 μF

9 V

18V

C₂=4 μF

3 μF

6 μF

2 μF

20 of 155

3 μF

21 of 155

8 V

V

C

22 of 155

10 V

1 μF

2 μF

3 μF

7 μF

10 V

1 μF

3 μF

7 μF

10 V

1 μF

10 V

23 of 155

12 V

C₄

C₃

C₂

C₁

C₂

C₃

12 V

C₄

12 V

C₄

C₃

C₂

C₁

C₅

12 V

C₁

C₂

C₃

24 of 155

C₁=3 μF

C₂=6 μF

C₃=6 μF

12 V

C₄=4 μF

12 V

C₁=2.0 μF

C₂=1.0 μF

C₃=1.0 μF

12 V

3 μF

6 μF

12 V

25 of 155

3 μF

6 μF

2 μF

12 V

2 μF

26 of 155

C₁=

2.0 μF

100 V

C₅=20.0 μF

C₂=

3.0 μF

C₃=

10.0 μF

C₄=

10.0 μF

27 of 155

12 V

C₄=

2.0 μF

C₅=

1.0 μF

C₆=

3.0 μF

C₃=

2.0 μF

C₂=

1.0 μF

C₁=2.0 μF

28 of 155

12 V

C₁=6.0 μF

C₂=4.0 μF

C₃=1.0 μF

C₄=2.0 μF

C₅=2.0 μF

12 V

C₁=6.0 μF

C₂=4.0 μF

C₃=1.0 μF

C_4,5=4.0 μF

12 V

C₁=6.0 μF

C₃=1.0 μF

C_2,4,5=2.0 μF

12 V

C₁=6.0 μF

C_2,3,4,5=3.0 μF

12 V

C_eq=2.0 μF

29 of 155

12 V

6.0 μF

4.0 μF

1.0 μF

4.0 μF

12 V

4.0 μF

1.0 μF

3.0 μF

6.0 μF

2.0 μF

30 of 155

12 V

C₂=

4 μF

C₁=

2 μF

C₃=

4 μF

C₄=

4 μF

C₅=

4 μF

C₆=

10 μF

	C_eq=
V₁=	Q₁=
V₂=	Q₂=
V₃=	Q₃=
V₄=	Q₄=
V₅=	Q₅=
V₆=	Q₆=

31 of 155

12 V

4.0 μF

1.0 μF

4.0 μF

32 of 155

12 V

1.0 μF

3.0 μF

A B C

33 of 155

4.0 μF

34 of 155

12 V

6.0 μF

3.0 μF

1.0 μF

6.0 μF

35 of 155

12 V

C₁=4.0 μF

C₂=4.0 μF

C₃=

1.0 μF

C₄=2.0 μF

C₅=

4.0 μF

C₆=

2.0 μF

36 of 155

12 V

C₁=6.0 μF

C₂=4.0 μF

C₃=1.0 μF

C₄=2.0 μF

C₅=2.0 μF

37 of 155

C₁=3.0 μF

C₃=1.0 μF

12 V

C₄=6.0 μF

C₆=2.0 μF

C₅=2.0 μF

C₂=3.0 μF

C₇=2.0 μF

38 of 155

2 V

C=10 μF

12 V

C₂=

6.0 μF

C₃=4.0 μF

C₁=2.0 μF

12 V

C₂=

2.0 μF

C₃=1.0 μF

C₁=3.0 μF

C₁=4.0 μF

C₃=4.0 μF

C₂=4.0 μF

C₄=3.0 μF

12 V

39 of 155

6.00 mF

12.0 mF

18 V

24.0 mF

3.00 mF

40 of 155

4.0 μF

2.0 μF

12 V

4.0 μF

3.0 μF

6.0 μF

2.0 μF

12 V

C₁=4.0 μF

C₂=3.0 μF

C₃=6.0 μF

C₄=2.0 μF

12 V

41 of 155

4.0 μF

3.0 μF

6.0 μF

2.0 μF

12 V

3 μF

6.0 μF

2.0 μF

12 V

42 of 155

3.0 μF

6.0 μF

2.0 μF

12 V

C₁

12 V

C₂

C₃

C

V

C

C₁

12 V

C₂

C₃

12 V

4 µF

6 µF

3 µF

43 of 155

8 V

C₁

44 of 155

18.0 V

3.00 µF

6.00 µF

12.0 µF

24.0 µF

45 of 155

C₁=

2.0 μF

100 V

C₅=20.0 μF

C₂=

3.0 μF

C₃=

10.0 μF

C₄=

10.0 μF

46 of 155

C₁=

3.0 μF

12 V

C₅=3.0 μF

C₂=

2.0 μF

C₃=

2.0 μF

C₄=

2.0 μF

47 of 155

48 of 155

Resistors in Series and Parallel

49 of 155

V

V₂

V₁

50 of 155

+

-

I

+

-

+

-

2 Ω

4 V

4 Ω

8 V

51 of 155

+

-

I

A

+

-

V

Red

Black

Red

Black

52 of 155

+

-

+

-

53 of 155

I

V

Ohmic

Slope=1/R

I

V

Non-ohmic

I

V

54 of 155

+

-

I

V

R

+

-

24 V

2 Ω

55 of 155

Wire A

Wire B

56 of 155

57 of 155

+

-

R

58 of 155

59 of 155

+

-

r

+

-

ε

60 of 155

61 of 155

+

-

ε

R

r

62 of 155

ΔV

R₂

R₁

I

V_in=10 V

R

V_out=5 V

63 of 155

+

-

R₂

R₁

64 of 155

A

R₁

V

2V

B

C

D

65 of 155

A

R₁

V

B

C

D

66 of 155

12 V

+

-

R₂

R₁

67 of 155

12 V

18 V

6.6Ω

1Ω

2.0 Ω

68 of 155

10 V

R₁=1Ω

R₂=2Ω

R₃=2Ω

I

69 of 155

10 V

R₁=1Ω

R₂=2Ω

R₃=2Ω

12 V

R₁=2.0Ω

R₂=4.0Ω

R₃=6.0Ω

70 of 155

V

R₁

R₂

I

I₂

I₁

4 V

2 Ω

71 of 155

12 V

3Ω

72 of 155

R₁=4 Ω

R₂=6 Ω

R₅=2 Ω

ε

R₃= 1 Ω

R₄=2 Ω

73 of 155

3 A

7 A

2 A

I=?

74 of 155

10 V

P₁=100 W

R₂

R₁

P₂=50 W

10 V

R₁=10Ω

R₂=20Ω

75 of 155

V=10 V

R₁=2Ω

R₂=4Ω

I

I₂

I₁

V=12 V

R₁=3Ω

R₂=6Ω

12 V

R₁=1Ω

R₂=2Ω

R₃=3Ω

I₁=______ , V₁=______

I₂=______ , V₂=______

I₃=______ , V₃=______

I₁=______ , V₁=______

I₂=______ , V₂=______

76 of 155

½ Ω

2 Ω

R

¼ Ω

77 of 155

R₁=3 Ω

R₂=6 Ω

R₃=2 Ω

12 V

R₁

R₅

R₄

R₂

R₃

R₁=3 Ω

R₂=6 Ω

R₃=2 Ω

V=?

V=4 V

R₁=2Ω

R₅=3Ω

R₄=4Ω

R₂=2Ω

R₃=2Ω

78 of 155

R₁=4 Ω

R₂=4 Ω

R₃=1 Ω

V=10 V

R₁=3 Ω

R₂=6 Ω

R₃=1 Ω

V=?

V₃=6 V

R₁=3 Ω

R₂=6 Ω

R₃=2 Ω

V=12 V

79 of 155

2 Ω

10 Ω

4 Ω

12 V

2 Ω

2.0 Ω

1.0 Ω

2.0 Ω

2.0 V

4.0 V

2.0 Ω

1.0 Ω

2.0 Ω

2.0 V

4.0 V

I₁

I₂

I₃

80 of 155

R₁=2Ω

1 Ω

I₁

2 Ω

12 V

81 of 155

R₁

I₁

12 V

R₂

R₃

S

82 of 155

I

83 of 155

R₁

R₂

84 of 155

3 Ω

ε

R₁=10 Ω

5 Ω

4 Ω

85 of 155

R₁=2 Ω

R₅=6 Ω

12 V

R₂=1 Ω

R₃=1 Ω

R₄=1 Ω

86 of 155

R₁=3 Ω

R₅=3 Ω

10 V

R₂=3 Ω

R₃=6 Ω

R₄=4 Ω

87 of 155

2.0 Ω

4.0 Ω

6.0 V

V=?

88 of 155

R₁=4 Ω

R₂=6 Ω

R₃=3 Ω

V=12V

I₁=	V₁=	P₁=
I₂=	V₂=	P₂=
I₃=	V₃=	P₃=

89 of 155

R₁=2 Ω

R₂=6 Ω

R₃=3 Ω

90 of 155

R₁=4 Ω

R₂=6 Ω

R₅=2 Ω

10 V

R₃= 1 Ω

R₄=2 Ω

R₁=1 Ω

R₂=6 Ω

R₅=2 Ω

R₃= 1 Ω

R₄=2 Ω

91 of 155

R₁=1 Ω

R₂=2 Ω

R₅=4 Ω

12 V

R₃= 2 Ω

R₄=2 Ω

R₆=5 Ω

R₈=8 Ω

R₇=3 Ω

92 of 155

R₁=12 Ω

R₂=4 Ω

R₅=1 Ω

10 V

R₃= 2 Ω

R₄=4 Ω

93 of 155

R₁=4 Ω

R₂=6 Ω

R₅=2 Ω

10 V

R₃= 1 Ω

R₄=2 Ω

94 of 155

R₁=3 Ω

R₂=3 Ω

R₅=3 Ω

12 V

R₃= 1 Ω

R₄=2 Ω

95 of 155

R₁

R₂

R₄

V

R₃

I₁

I₂

I₃

I₄

96 of 155

3 Ω

2 Ω

V

6 Ω

6 V

97 of 155

R₃=2 Ω

R₄=2 Ω

R₅=2 Ω

R₁=2 Ω

R₂=2 Ω

12 V

R₄=2 Ω

R₅=2 Ω

R₆=5 Ω

R₂=2 Ω

R₃=1 Ω

12 V

R₁=

2 Ω

98 of 155

R₄=3 Ω

R₅=6 Ω

R₆=1 Ω

R₂=2 Ω

R₃=4 Ω

12 V

R₁=

2 Ω

99 of 155

R₄=3 Ω

R₅=6 Ω

R₆=2 Ω

R₂=3 Ω

R₃=1 Ω

12 V

R₁=

2 Ω

100 of 155

2 Ω

12 V

1 Ω

6 Ω

2 Ω

101 of 155

R₁=3 Ω

R₂=6 Ω

R₃=2 Ω

12 V

102 of 155

R₁=1 Ω

R₂=3 Ω

R₃=6 Ω

V=12 V

R₁=1 Ω

V=12 V

R₁₂₃=1 Ω+2 Ω=3 Ω

V=12 V

103 of 155

R₃=6 Ω

V=12 V

R₁=1 Ω

R₂=2 Ω

6 Ω

V=?

1 Ω

2 Ω

3 V

104 of 155

R₁=4 Ω

R₂=6 Ω

R₅=2 Ω

ε

R₃= 1 Ω

R₄=2 Ω

R₁=2 Ω

R₂=6 Ω

R₅=2 Ω

9 V

R₃= 1 Ω

R₄=2 Ω

105 of 155

Multiloop Circuits

106 of 155

2 Ω

1 Ω

2 V

4 V

I₁=___________

I₂=___________

I₃=___________

107 of 155

1 Ω

2 Ω

2 V

4 V

3 Ω

2 Ω

1 Ω

12 V

5 V

4 V

I₁

I₂

I₃

I₁=___________

I₂=___________

I₃=___________

108 of 155

3 Ω

2 Ω

1 Ω

12 V

5 V

4 V

3 Ω

2 Ω

1 Ω

12 V

5 V

4 V

I₁

I₂

I₃

I₁=___________

I₂=___________

I₃=___________

3 Ω

2 Ω

12 V

6 V

4 V

109 of 155

3 Ω

2 Ω

1 Ω

12 V

5 V

4 V

3 Ω

2 Ω

1 Ω

12 V

5 V

4 V

I₁

I₂

I₃

I₁=___________

I₂=___________

I₃=___________

2 Ω

3 Ω

4 Ω

12 V

6 V

4 V

I₁

I₂

I₃

110 of 155

3 V

2 Ω

5 V

6 Ω

6 V

I₁

I₂

I₃

14 V

4 Ω

10 V

6 Ω

6 V

I₁

I₂

I₃

I₁=___________

I₂=___________

I₃=___________

111 of 155

4 V

2 Ω

8 V

6 Ω

2 V

I₁

I₂

I₃

I₁=_____ (left or right)

I₂=_____ (left or right)

I₃=_____ (left or right)

4 V

2 Ω

8 V

6 Ω

2 V

I₁

I₂

I₃

A. I₁=I₂+ I₃

B. 4-2I₁-8+6I₂=0

C. 4I₁-2I₁+2I₃=0

D. 8+2-6I₂=0

112 of 155

4 V

2 Ω

8 V

6 Ω

2 V

I₁

I₂

I₃

I₁=_____ (left or right)

I₂=_____ (left or right)

I₃=_____ (left or right)

3 V

2 Ω

8 V

5 Ω

2 V

I₁

I₂

I₃

A. I₁+I₃=I₂

B. -2 I₁-8-5 I₂+3=0

C. 8-2+5 I₂=0

D. -3+5 I₂+8+2 I₁=0

113 of 155

4 V

2 Ω

3 V

6 Ω

6 V

114 of 155

10 V

4 Ω

2 V

3 Ω

4 V

I₁

I₂

I₃

I₁=___________

I₂=___________

I₃=___________

115 of 155

10 V

I₁

I₂

I₃

12 V

20 V

3 Ω

A

4 Ω

1 Ω

10 V

12 V

1 Ω

2 Ω

5 Ω

4 V

12 V

1 Ω

2 Ω

6 V

116 of 155

3 V

2 Ω

5 V

6 Ω

6 V

I₁

I₂

I₃

I₁=___________; left or right

I₂=___________; left or right

I₃=___________; left or right

117 of 155

1 Ω

2 Ω

2 V

4 V

3 Ω

2 Ω

1 Ω

12 V

5 V

4 V

I₁

I₂

I₃

I₁=___________

I₂=___________

I₃=___________

1 Ω

2 Ω

6 V

1 V

2 V

I₁=___________

I₂=___________

I₃=___________

118 of 155

V₁

I₁

I₂

I₃

V₃

V₂

R₁

R₂

R₃

10 V

I₁

I₂

I₃

15 V

5 V

2 Ω

3 Ω

4 Ω

119 of 155

2 V

I₁

I₂

1 V

3 Ω

4 Ω

I₃

I₁=___________ (up or down)

I₂=___________ (up or down)

I₃=___________ (up or down)

120 of 155

3 Ω

2 Ω

1 Ω

12 V

5 V

4 V

3 Ω

2 Ω

1 Ω

12 V

5 V

4 V

I₁

I₂

I₃

I₁=___________

I₂=___________

I₃=___________

121 of 155

1 Ω

2 Ω

2 V

4 V

I₁=___________

I₂=___________

I₃=___________

I₁

I₂

I₃

122 of 155

2 Ω

8 V

4 V

2 V

I₁

I₂

I₃

I₁=___________

I₂=___________

I₃=___________

14 V

4 Ω

10 V

6 Ω

6 V

I₁

I₂

I₃

I₄

I₅

I₆

4 Ω

3 Ω

8 V

2 V

1 V

I₁

I₂

I₃

I₁=___________ up or down

I₂=___________ up or down

I₃=___________ up or down

123 of 155

14 V

R₂=4 Ω

10 V

R₁=6 Ω

R₃=2 Ω

14 V

R₂=4 Ω

10 V

R₁=6 Ω

R₃=2 Ω

I₁

I₃

I₂

124 of 155

1 V

I₁

I₂

I₃

125 of 155

I₁

I₂

I=?

I₅

I₄

I₆

12A

4A

5A

6A

3 A

12A

4A

5A

6A

2A

I

126 of 155

I₁

I₂

I₃

I₄

I₅

I₆

6A

I₁

8A

I₃

I₂

3A

12 V

6 V

1 Ω

2 Ω

127 of 155

R_a

V=10V

R_b

R_x

R

I_a

I_b

I

I_x

I_g

128 of 155

A

R_s

1 A

9 A

R_L

G

Components of a Voltmeter

G

R_s

Components of an Ammeter

129 of 155

I

I₁

I₂

I=I₁+I₂

I=?

10 A

5 A

20 A

130 of 155

I

I₁

I₂

I=I₁+I₂

4 A

8 A

2 A

I=?

12 A

2 A

I=?

1 A

131 of 155

V

I

R

a

b

I

R

a

b

a

b

ε

+

-

a

b

ε

+

-

132 of 155

V

R

a

b

I

R

a

b

a

b

ε

+

-

a

b

ε

+

-

133 of 155

V

C

R

12 V

1 µF

2 MΩ

134 of 155

current

time

current

time

current

time

current

time

A

B

C

D

voltage

time

voltage

time

voltage

time

voltage

time

A

B

C

D

charge

time

charge

time

charge

time

charge

time

A

B

C

D

135 of 155

voltage

time

voltage

time

voltage

time

voltage

time

D

C

B

A

charge

time

charge

time

charge

time

charge

time

D

C

B

A

136 of 155

time

Charging Discharging

Charge

time

Voltage

time

Current

Charge

time

137 of 155

C

R

current

time

current

time

current

time

current

time

A

B

C

D

138 of 155

2 Ω

6 V

1 Ω

1 F

1 Ω

6 V

1 Ω

1 F

1 Ω

139 of 155

6.00 V

2.00 MΩ

3.00 μF

6.00 V

4.00 MΩ

3.00 μF

10.0 V

5.00 MΩ

2.00 μF

140 of 155

Home Circuits

141 of 155

4 Ω

6 V

1 Ω

1 F

1 Ω

142 of 155

143 of 155

Meter

hot

neutral

Circuit

Breaker

144 of 155

145 of 155

Appliance

146 of 155

147 of 155

× × × × × × × × × × × × ×

2 V

V₂

∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙

× × × × × × × × × × × × ×

148 of 155

∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙

10 V

∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙

2 Ω

∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙

10 V

∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙

149 of 155

× × × ×

× × × × × × × × × × × × ×

V

V₂

∙ ∙ ∙ ∙

10 cm

150 of 155

12 V

2 Ω

3 H

1μF

3 mH

10.0 V

2.0 Ω

6μF

30 mH

a

b

12 V

3 Ω

8 H

2 μF

400 Ω

6 H

151 of 155

a

b

c

d

152 of 155

I

II

III

IV

153 of 155

I

II

III

IV

154 of 155

R₁=4 Ω

R₂=6 Ω

R_a

V=10V

R_b

R_x

R

I_a

I_b

I

I_x

I_g

155 of 155

A

R_s

1 A

9 A

R_L=5000 Ω

V

R_V=5000 Ω

V

R_V=5000 Ω

A

10 A

A

R_s