scans of circuits

MINOLOGY

source

1sion

e-throw ,Je-throw

)City

d

ments that

mected in

PROBLEMS

Figure Pl.S: Circuit for Problem 1.5.

1.6 For the circuit in Fig. P1.6: (a) Identify and label all distinct nodes. (b) Which of those nodes are extraordinary nodes? (c) Identify all combinations of2 or more circuit elements that

are connected in series. (d) Identify pairs of circuit elements that are connected in

parallel.

Figure P1.6: Circuit for Problem 1.6.

1.7 For the circuit in Fig. P1.7:

(a) Identify and label all distinct nodes. (b) Which of those nodes are extraordinary nodes? (c) Identify all combinations of 2 or more circuit elements that


parallel.

lQ

4V +


43

1.8 For the circuit in Fig. Pl.S: (a) Identify and label all distinct nodes. (b) Which of those nodes are extraordinary nodes? (c) Identify all combinations of2 or more circuit elements that


parallel.

25 n

60Q

15 n

Figure Pl.8: Circuit for Problem 1.8.

1.9 For the circuit in Fig. P1.9: (a) Identify and label all distinct nodes. (b) Which of those nodes are extraordinary nodes? (c) Identify all combinations of2 or more circuit elements that


parallel.

4A

2Q 4Q

Figure Pl.9: Circuit for Problem 1.9.

1.10 For the circuit in Fig. PLIO: (a) Identify and label all distinct nodes . (b) Which of those nodes are extraordinary nodes? (c) Identify all combinations of2 or more circuit elements that

are connected in series.

4 4

( d ) I d e n t i f y p a i r s o f c i r c u i t e l e m e n t s t h a t a r e c o n n e c t e d i n

p a r a l l e l .

8 Q

1 2 V ( T } 4Q~ ""'-16Q~ 6 Q

F i g u r e P l . l O : C i r c u i t f o r P r o b l e m 1 . 1 0 .

1 . 1 1 F o r t h e c i r c u i t i n F i g . P l . l l :

( a ) I d e n t i f y a n d l a b e l a l l d i s t i n c t n o d e s .

( b ) W h i c h o f t h o s e n o d e s a r e e x t r a o r d i n a r y n o d e s ?

( c ) I d e n t i f y a l l c o m b i n a t i o n s o f 2 o r m o r e c i r c u i t e l e m e n t s t h a t

a r e c o n n e c t e d i n s e r i e s .

( d ) I d e n t i f y p a i r s o f c i r c u i t e l e m e n t s t h a t a r e c o n n e c t e d i n

p a r a l l e l .

F i g u r e P l . l l : C i r c u i t f o r P r o b l e m 1 . 1 1 .

1 . 1 2 T h e t o t a l c h a r g e c o n t a i n e d i n a c e r t a i n r e g i o n o f s p a c e

i s - 1 C . I f t h a t r e g i o n c o n t a i n s o n l y e l e c t r o n s , h o w m a n y d o e s

i t c o n t a i n ?

* 1 . 1 3 A c e r t a i n c r o s s s e c t i o n l i e s i n t h e x - y p l a n e . I f 3 x 1 0

2 0

e l e c t r o n s g o t h r o u g h t h e c r o s s s e c t i o n i n t h e z d i r e c t i o n i n 4

s e c o n d s , a n d s i m u l t a n e o u s l y 1 . 5 x 1 0

2 0

p r o t o n s g o t h r o u g h

t h e s a m e c r o s s s e c t i o n i n t h e n e g a t i v e z d i r e c t i o n , w h a t i s t h e

m a g n i t u d e a n d d i r e c t i o n o f t h e c u r r e n t f l o w i n g t h r o u g h t h e c r o s s

s e c t i o n ?

1 . 1 4 D e t e r m i n e t h e c u r r e n t i ( t ) f l o w i n g t h r o u g h a r e s i s t o r i f

t h e c u m u l a t i v e c h a r g e t h a t h a s f l o w e d t h r o u g h i t u p t o t i m e t i s

g i v e n b y

C H A P T E R 1 C I R C U I T T E R M I N O L O G Y

( a ) q ( t ) = 3 . 6 t m C

( b ) q ( t ) = 5 s i n ( 3 7 7 t ) p . , C

* ( c ) q ( t ) = 0 . 3 [ 1 - e -

0

. 4

1

] p C

( d ) q ( t ) = 0 . 2 t s i n ( l 2 0 7 r t ) n C

1 . 1 5 D e t e r m i n e t h e c u r r e n t i ( t ) f l o w i n g t h r o u g h a c e r t a i n

d e v i c e i f t h e c u m u l a t i v e c h a r g e t h a t h a s f l o w e d t h r o u g h i t u p t o

t i m e t i s g i v e n b y

( a ) q ( t ) = - 0 . 4 5 t

3

p . , C

( b ) q ( t ) = 1 2 s i n

2

( 8 0 0 m ) m C

( c ) q ( t ) = - 3 . 2 s i n ( 3 7 7 t ) c o s ( 3 7 7 t ) p C

* ( d ) q ( t ) = 1 . 7 t [ l - e - 1 .

2 1

] n C

1 . 1 6 D e t e r m i n e t h e n e t c h a r g e 1 1 Q t h a t f l o w e d t h r o u g h a

r e s i s t o r o v e r t h e s p e c i f i e d t i m e i n t e r v a l f o r e a c h o f t h e f o l l o w i n g

c u r r e n t s :

( a ) i ( t ) = 0 . 3 6 A , f r o m t = 0 t o t = 3 s

* ( b ) i ( t ) = [ 4 0 t + 8 ] r n A , f r o m t = 1 s t o t = 1 2 s

( c ) i ( t ) = 5 s i n ( 4 7 r t ) n A , f r o m t = 0 t o t = 0 . 0 5 s

( d ) i ( t ) = 1 2 e -

0

3 1

r n A , f r o m t = 0 t o t = o o

1 . 1 7 D e t e r m i n e t h e n e t c h a r g e 1 1 Q t h a t f l o w e d t h r o u g h a

c e r t a i n d e v i c e o v e r t h e s p e c i f i e d t i m e i n t e r v a l s f o r e a c h o f t h e

f o l l o w i n g c u r r e n t s :

( a ) i ( t ) = [ 3 t + 6 t

3

] r n A , f r o m t = 0 t o t = 4 s

* ( b ) i ( t ) = 4 s i n ( 4 0 7 r t ) c o s ( 4 0 7 r t ) p . , A , f r o m t = 0 t o

t = 0 . 0 5 s

( c ) i ( t ) = [ 4 e - t - 3 e -

2 1

] A , f r o m t = 0 t o t = o o

( d ) i ( t ) = 1 2 e -

3 1

c o s ( 4 0 7 r t ) n A , f r o m t = 0 t o t = 0 . 0 5 s

1 . 1 8 I f t h e c u r r e n t f l o w i n g t h r o u g h a w i r e i s g i v e n b y

i ( t ) = 3 e -

0

1 1

r n A , h o w m a n y e l e c t r o n s p a s s t h r o u g h t h e w i r e ' s

c r o s s s e c t i o n o v e r t h e t i m e i n t e r v a l f r o m t = 0 t o t = 0 . 3 m s ?

1 . 1 9 T h e c u m u l a t i v e c h a r g e i n m C t h a t e n t e r e d a c e r t a i n

d e v i c e i s g i v e n b y

q ( t ) = ~~t

6 0 - t

f o r t < 0 ,

f o r 0 : : : : t : : : : 1 0 s ,

f o r 1 0 s : : : : t : : : : 6 0 s

( a ) P l o t q ( t ) v e r s u s t f r o m t = 0 t o t = 6 0 s .

( b ) P l o t t h e c o r r e s p o n d i n g c u r r e n t i ( t ) e n t e r i n g t h e d e v i c e .

* 1 . 2 0 A s t e a d y f l o w r e s u l t e d i n 3 x 1 0

1 5

e l e c t r o n s e n t e r i n g a

d e v i c e i n 0 . 1 m s . W h a t i s t h e c u r r e n t ?

P R O

1 . 2 1

g i v e n

( a ) ,

( b )

1 . 2 2

o f c h

-OGY

!rtain up to

~h a 1ing

1 a

the

to

'Y 's

?

n

PROBLEMS

1.21 Given that the current in (rnA) flowing through a wire is given by:

i (t) = 6t for 0 _:::: t _:::: 5 s 10 fort < 0

30e-06

4 6

v

3

= 6 V

R 2 I I

1 0 v { : )

I ~

R ,

I

V

2

= 4 V

I

2 o v { )

J

I I

R 3

v

4

= 1 2 v

F i g u r e P 1 . 2 6 : q ( t ) f o r P r o b l e m 1 . 2 6 .

1 . 2 7 F o r e a c h o f t h e e i g h t d e v i c e s i n t h e c i r c u i t o f F i g . P 1 . 2 7 ,

d e t e r m i n e w h e t h e r t h e d e v i c e i s a s u p p l i e r o r a r e c i p i e n t o f

p o w e r a n d h o w m u c h p o w e r i t i s s u p p l y i n g o r r e c e i v i n g .

+ 6 V -

2

+

l O Y 1 3

6

+ 1 2 V -

- 7 V +

8

F i g u r e P 1 . 2 7 : C i r c u i t f o r P r o b l e m 1 . 2 7 .

3 A +

9 V I 7

+

1 . 2 8 F o r e a c h o f t h e s e v e n d e v i c e s i n t h e c i r c u i t o f F i g . P 1 . 2 8 ,

d e t e r m i n e w h e t h e r t h e d e v i c e i s a s u p p l i e r o r a r e c i p i e n t o f

p o w e r a n d h o w m u c h p o w e r i t i s s u p p l y i n g o r r e c e i v i n g .

* 1 . 2 9 A n e l e c t r i c o v e n o p e r a t e s a t 1 2 0 V . I f i t s p o w e r r a t i n g i s

0 . 6 k W , w h a t a m o u n t o f c u r r e n t d o e s i t d r a w , a n d h o w m u c h

e n e r g y d o e s i t c o n s u m e i n 1 2 m i n u t e s o f o p e r a t i o n ?

1 . 3 0 A 9 V f l a s h l i g h t b a t t e r y h a s a r a t i n g o f 1 . 8 k W h . I f

t h e b u l b d r a w s a c u r r e n t o f 1 0 0 r n A w h e n l i t ; d e t e r m i n e t h e

f o l l o w i n g :

( a ) F o r h o w l o n g w i l l t h e f l a s h l i g h t p r o v i d e i l l u m i n a t i o n ?

I

I

I

I

C H A P T E R 1 C I R C U I T T E R M I N O L O G Y

+ 6 V -

I

~

s A t

+

2 4 v

I

X~'\

/ " _ X


( b ) H o w m u c h e n e r g y i n j o u l e s i s c o n t a i n e d i n t h e b a t t e r y ?

( c ) W h a t i s t h e b a t t e r y ' s r a t i n g i n a m p e r e - h o u r s ?

I ~

1 . 3 1 T h e v o l t a g e a c r o s s a n d c u r r e n t t h r o u g h a c e r t a i n d e v i c e

a r e g i v e n b y

v ( t ) = 5 c o s ( 4 n t ) V ,

i ( t ) = 0 . 1 c o s ( 4 n t ) A .

D e t e r m i n e :

* ( a ) T h e i n s t a n t a n e o u s p o w e r p ( t ) a t t = 0 a n d t = 0 . 2 5 s .

( b ) T h e a v e r a g e p o w e r P a v . d e f i n e d a s t h e a v e r a g e v a l u e o f

p ( t ) o v e r a f u l l t i m e p e r i o d o f t h e c o s i n e f u n c t i o n ( 0 t o

0 . 5 s ) .

1 . 3 2 T h e v o l t a g e a c r o s s a n d c u r r e n t t h r o u g h a c e r t a i n d e v i c e

a r e g i v e n b y

v ( t ) = 1 0 0 ( 1 - e -

0

-

2 1

) V ,

i ( t ) = 3 0 e -

0 2 1

r n A .

D e t e r m i n e :

( a ) T h e i n s t a n t a n e o u s p o w e r p ( t ) a t t = 0 a n d t = 3 s .

( b ) T h e c u m u l a t i v e e n e r g y d e l i v e r e d t o t h e d e v i c e f r o m t = 0

t o t = o o .

1 . 3 3 T h e v o l t a g e a c r o s s a d e v i c e a n d t h e c u r r e n t t h r o u g h i t

a r e s h o w n g r a p h i c a l l y i n F i g . P 1 . 3 3 . S k e t c h t h e c o r r e s p o n d i n g

p o w e r d e l i v e r e d t o t h e d e v i c e a n d c a l c u l a t e t h e e n e r g y a b s o r b e d

b y i t .

1 . 3 4 T h e v o l t a g e a c r o s s a d e v i c e a n d t h e c u r r e n t t h r o u g h i t

a r e s h o w n g r a p h i c a l l y i n F i g . P 1 . 3 4 . S k e t c h t h e c o r r e s p o n d i n g

p o w e r d e l i v e r e d t o t h e d e v i c e a n d c a l c u l a t e t h e e n e r g y a b s o r b e d

b y i t .

I

5

IVE CIRCUITS

ill 10 em

m

:50

50

PROBLEMS 103

what fraction of the power generated by the generating station *2.15 Determine Ix in the circuit of Fig. P2.15. is used by the city.

RL (city)

Figure P2.12: Diagram for Problem 2.12.

2.13 Determine the current I in the circuit of Fig. P2.13 given that Io = 0.

3Q

24 v +


2.14 Determine currents I 1 to I3 in the circuit of Fig. P2.14.

IA

2Q

70


Figure P2.15: Circuit for Problem 2.15 .

2.16 Determine currents It to I4 in the circuit of Fig. P2.16.

5V


*2.17 Determine currents I 1 to !4 in the circuit of Fig. P2.17.

6A


2.18 Determine the amount of power dissipated in the 3 kQ resistor in the circuit of Fig. P2.18.

Figure P2,18: Circuit for Pro~lem 2.18.

1 0 4

* 2 . 1 9

D e t e r m i n e f x a n d f y i n t h e c i r c u i t o f F i g . P 2 . 1 9 .

2 Q

1

x 6 n I y

.---~NV' ~ N V ' . . . . . . . . .

w v e ! ) f n ~4I,


2 . 2 0 F i n d V a b i n t h e c i r c u i t o f F i g . P 2 . 2 0 .

2 Q

a

+

V a b

b


2 . 2 1 F i n d /

1

t o f ) i n t h e c i r c u i t o f F i g . P 2 . 2 1 .

8 V

!

1

! 3

3 k Q - - - +

~

~h

4 k Q

2 k Q


2 . 2 2 F i n d I i n t h e c i r c u i t o f F i g . P 2 . 2 2 .

~ ~~----~

l O V e ! ) ~30


* 2 . 2 3 D e t e r m i n e t h e a m o u n t o f p o w e r s u p p l i e d b y t h e

i n d e p e n d e n t c u r r e n t s o u r c e i n t h e c i r c u i t o f F i g . P 2 . 2 3 .

C H A P T E R 2 R E S I S T I V E C I R C U I T S

02A~ ~~~:~ f~l


2 . 2 4 G i v e n t h a t i n t h e c i r c u i t o f F i g . P 2 . 2 4 , /

1

= 4 A

/ 2 = I A , a n d / 3 = 1 A , d e t e r m i n e n o d e v o l t a g e s v , , V 2 , a n d V J

I

1

. . 1 . . - R , = 1 8 n

- -

-

! 3


v3

1 8 n

* 2 . 2 5 A f t e r a s s i g n i n g n o d e V 4 i n t h e c i r c u i t o f F i g . P 2 . 2 5 i l l

t h e g r o u n d n o d e , d e t e r m i n e n o d e v o l t a g e s v , , V 2 , a n d V 3 .

3 A

1 2 v

- -

_ _ _ , L N V ' ! V 3

v , ; N V ' ' 6 n

-

l A

V 4

6 Q

-

l A

F i g u r e P 2 . 2 5 : C i r c u i t f o r P r o b l e m s 2 . 2 5 a n d 2 . 2 6 .

2 . 2 6 A f t e r a s s i g n i n g n o d e V

1

i n t h e c i r c u i t o f F i g . P 2 . 2 5 a '

t h e g r o u n d n o d e , d e t e r m i n e n o d e v o l t a g e s V 2 , V 3 , a n d V 4 .

2 . 2 7 I n t h e c i r c u i t o f F i g . P 2 . 2 7 , / 1 = 4 2 / 8 1 A

/ 2 = 4 2 / 8 1 A , a n d / 3 = 2 4 / 8 1 A . D e t e r m i n e n o d e voltag~

V 2 , V 3 , a n d V 4 a f t e r a s s i g n i n g n o d e v , a s t h e g r o u n d n o d e .

P R O B L E M S

V J E I

9 0 h

-

p o w e r .

S e c t i o n 2 - 3 :

2 . 2 9 G i v e n l

d e t e r m i n e I o .

I o

2 . 3 0 W h a t

R e q = 4 Q ?

a

R e q

b

I i l l

1 0 6

2 . 3 5 I f R = 1 2 r . ! i n t h e c i r c u i t o f F i g . P 2 . 3 S , f i n d I .


* 2 . 3 6 U s e r e s i s t a n c e r e d u c t i o n a n d s o u r c e t r a n s f o r m a t i o n t o

f i n d V x i n t h e c i r c u i t o f F i g . P 2 . 3 6 . A l l r e s i s t a n c e v a l u e s a r e i n

o h m s .

4 + V : y -

~....----16 - - - - . . F v i 1 2 ( ! ) 1 o A i 6 ~'---r6 i - - - - - , 1 6 }


2 . 3 7 D e t e r m i n e A i f V o u t ! V

5

= 9 i n t h e c i r c u i t o f F i g . P 2 . 3 7 .

3 0

1 2 Q

p ,

1 2 0

3 0


+

6 0 V o u t

* 2 . 3 8 F o r t h e c i r c u i t i n F i g . P 2 . 3 8 , f i n d R e q a t t e r m i n a l s ( a , b ) .

~0-------r---NV------;----vvv-~ c

3 0 5 0

I b e 6 0 3 0 d

L F i g u r e P 2 . 3 8 : C i r c u i t f o r P r o b l e m s 2 . 3 8 a n d 2 . 3 9 .

C H A P T E R 2 R E S I S T I V E C I R C U I

2 . 3 9 F i n d R e q a t t e r m i n a l s ( c , d ) i n t h e c i r c u i t o f F i g . P 2

2 . 4 0 S i m p l i f y t h e c i r c u i t t o t h e r i g h t o f t e r m i n a l s ( a , b )

F i g . P 2 . 4 0 t o f i n d R e q . a n d t h e n d e t e r m i n e t h e a m o u n t ofpo~

s u p p l i e d b y t h e v o l t a g e s o u r c e . A l l r e s i s t a n c e s a r e i n o h m s .

a

b


2 . 4 1 F o r t h e c i r c u i t i n F i g . P 2 . 4 1 , d e t e r m i n e R e q a t

* ( a ) T e r m i n a l s ( a , b )

( b ) T e r m i n a l s ( a , c )

( c ) T e r m i n a l s ( a , d )

( d ) T e r m i n a l s ( a , f )

I

2 0

d o - A N I - A N I

2 0

c o - A N I - A N I


I

2 0

2 0

2 0

b

2 . 4 2 F i n d R e q f o r t h e c i r c u i t i n F i g . P 2 . 4 2 . A l l r e s i s t a n c e s a r c

i n o h m s .

R , q - : ~ 10~

5 1 0


2 . 4 3

t h e c

2 . 4 4

t o

i n t o

( a ,

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