'

ELECTRIC CIRCUITS II

ASSIGNMENT I

One of the questions included in this document shall be selected for in class assignment that will be conducted during the week of

Feb 29, 2020 - March 5, 2020

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Question (1) In the circuit shown in Figure 1 the current magnitudes are known to be: h = 29.9A, 11 = 22.3A, and

h = 8.0 A. If the supply frequency is 60Hz, obtain the circuit constants Rand L.

' \Tr I - \CS \ I 2. \

- \S 'I.. '8

\ \ \rT \ - j ?..o ~\

I .I \ = \~11\\41 \

\ '1 I -I

'i, -

I 't. \ 'L (_-) -t ( _ ) =

R ' w L

I 'IT I -

+ c

\r_ I

\ ) "' wl

\ j\.~L

.. Ir

► R • ►

•► -

( I \ )1.. ~ -t I~ -t"

.,_ . 2

(-' ) ; ('2.'i .°\) WL 12.~

l •· l l2

I .. ► .. ; i«>L :~ 1s n ... ~

1

2. 1'5 "4<- _ o- o'l3i"1

\-R = 5".T1 SL J

' vJL

L -

-- 0 .Ob ~ I}

\

, 2 0,;: ( 0 _06-=t-1,)

"

Question (2)

In the network shown in Figure 2, the two equal capacitances C and the parallel resistance R arc

adjusted until the detector current Io is zero. Assuming a source angular frequency co, determine the

values of Rx and Lx.

C C --t> o A I I I I

I I --. +2-!- ! lo Is r,: i rs -:cl -= 0

Zs I

>J i ) Zo .~

v,cp Rx -~

:-,L

Figure 2

. , ~s~ Cvc-t'en-1- <liv,'5 ion :

- j Xe. - JX<-T I~

:1 - R- j X c. - j X. c.

k.\JL

~x -

- -Z.x I s

Lx Is

I -

- l - ) Xe.. ) I I - D

- J Xe. _L ,

(

- j Xe.. -j Xe.. ---

i< - j 'l.X c.

X l. C.

K - j 2 Xe. R -- - J ~l.

2x X 2. Xi. c., c.. Xe..

~ x~ \ ~x

\ ~ x - ----t:,. - - -1> - --R

~)( x"\.

(.. 4

'2. - \ Lx Xe... \ L~ - -t, =- ---t> -Xe... Wlx 2w

I

-

=

\ \ - ·+- -i<x Jwlx

\ 1

t 'Z, 'l. R we

\ l 2-w1.. C..

Question (3)

The circuit in Figure 3 is operating at sinusoidal steady state. The capacitor is adjusted until the

current lg is in phase with V g. Specify the capacitor in Microfarads if the phase angle between lg and

V g is 40° leading.

\r<t - -z._, 'I~

~-\- j ~ ·,~ ~

z~

--

-- jWL +

Figure 3

R ~ Jv.JC~ 1..

j -t (wcf<. )z.

'T j I WL -\ -t- l vJ c.,P- ) 'L L

LZ~

(i)L -1 + ( w c..RJ i

=-t>

'- 1 wcR

\ t ( Wc.1<. )"L

- CJ

L -+ L( w CR )1.. -= CR

C -'K :t J ~ ~ - 4 w~ it c-

2 w 2. ff· L

Y<>-<+ '2 'el'""" -ttcJ- ii;._ rhaS.e.. U'...__ ~~ l.\ 0 ~ LG>-.d.t~

Lz'i = e.,. - G, - - 40°

l"" l ~\ tOJ\ ( -40) =

Re.. 1. Z~J y.,_ \"zi 1 -h,,, c -\.\ 0 ) = __1_"' \ Li J ~ "tevl\ ~40)

\ -+- (wcR) 1.

WC R--i. wl ----­

\ + lW CR) ,_

K-\,~ (-4 o) = wL l \ + ( L-:>C: A.l·} - w c.. R "L,.

l "2. 'l. ' ( w L T wl we R ) - <...JC R - R. ~~ - 4 o) -=- <:)

[ c.,}--,;t L] C ,,_ + [ - G..)R 1 C. + ( wL - R -lov... l -40)] =- 0

wR = J ( -w~ ) "l.. - 4 ( w3 R"?. L) ( wL - R-b(-40))

1 u:l:, Q'- L

..

Question (4)

In the circuit shown in figure 4, i {t) = 10 sin t . Calculate the value of C such that v {t) = Vo sin t V. Find Vo.

1n r-----.------.....--",l\J\~

i(t) t +

1{1) l F C

w = 1 ,o.J. ls Figure 4

~~ \"

\.. l-t) -\iltl -

G

..l...

t i,.._.._ ~o~c.,.a~ -=-\> I" '? ho,.~0.- do(","\~..,..

Jo CS ,1' (~ ) T -

\jl) ~ \Y"I ( ~} V --

-- + . 2 J J

_ ~ \ I l • I + j Xe_

- j \ - j X~ \ ,,_ \ ~ i X c:.. l l

. I - j - -r

L.

j

\ + x~ c..

3o \re

\-t i ~ <:..

. t X, -r J

\ + X "\. c..

- G

-~io = 1c l- qo"

-~~ =- \ro L-9o~

U.si0 @ : 'fkse.. '«\ ".,J.;; 0 ~

.. L \/ = -la.V\-\ [I~\ ·Y-to\; \ l t--c~ot Re. 1 'f ~'c 1 ~

:. Trv-1 \ ~ "tot J =- c,

Xe_ l --\ + )<'l. 'l.

c..

'l Xe.. = \ + x~ x-z.. - 2. X '- + j - ~

C,

we_

\()

\To

o'.. \ . -s O _ 2 o ""J

Question (5) Figure 5 shows a Wien-bridge network. What is the frequency at which the phase shift between the

input and output signals is zero? What is the ratio Yo/ Yi at that freq uency.

7 - ~ T" I - ' J WC..

i<

.. \r . l-, L -

~, -tt<1. . \r· L'l. I -

zl -t -z,

Figure 5

I I

¥..\fl - \.r6 -I').7-, -t- "I,R1 -= Ci

-=-\f. 7, \f·

- \f, -r \ 0 I z , -t z.,.

\f"o R., "Z., - - R,-r (<..,,. \r- z, + z,.. \

R, 'R ,;-Ri.

for ze.ft) f'~C cs h\~-\- I(Y\ \ ¼ 1 = 0 \

K-1- \/jwc

R;- y -t R J'v)C. l T J t.vCR

~ J WC.

-

't. ( \ -t ~w c R)

-=

0

( j + )w e~) i. -r jwcR

. . \r-t

::i- w1.c'l R'.l ~ ) ':L.wC.~

1 - w '-c'l.. ~'" ;- j owc..R

"' ( 1 - w,.ct R1..) - S 3DJc.R

x ( (.1 - w"l.ci.R""t. ) - ~3wc.RJ

~ ( \ - 1.,:}-c 'L 'i<.' ) ~ ~ '.lwc.R 1 ~ (_ I - w..._ c"-fl_-... ) - j ~ w e,~

( \ - w"\..c.-i. ~ ) 1.. -t ( 3wCR ) 1...

.

( 1 - 1._,}-c_ 'L ~ ~ - ~?, w c_ ~ ( \ - w .._ C 1/ ) T j '.2.W cR ( I -w .,__ c' R ) + (j 2""<:.R) b;,, WQl.) "2.

:Irr> 1 ~i ~ = 0

7 ~ (

1 _ c,;-' c, .,_ f<. '- } -1--~ (1 - w'-C p_" ~ =- 0

"2.. t. 'l.. n, . ..._"2... c °t.. o"'L 0 - 3 -t 3 ~ c R ;- 'l. -, J...V'J " -

vf c., "Z. ~ "'L. - 1

1 w --

'KC

j j =

2-r::RC

\Jo

\f· I

'-.r· I

~, ~~1 z, ) 'i<' ~ R, z,-+ 2'L

R, ( "l.l-4. ) \-WC~ -+ b u)7.. c 1. R "l..

R, + R1.- ( \ -W1.. C 't. R."1.. ) ,_ -t ('~ v-JC R) "l..

Question (6) The ac bridge circuit of Figure 6 is called a Wien bridge. It is used for measuring the frequency of a

source. Find an expression for the supply frequency when the bridge is balanced .

.....------------ll \f"s

Figure 6

Ob L b,,d~e. ,~ boJO-K\C'.-'2- J 0

\;. C> \r°'- ·- \r b -:=. Qi =t> ~ - b o C

L.2. ~ L."' \Ts \r'S ::: Va. - -z..a + z\{ -z.., + -z'l.

L2 rz'1 --

72 -Z3 = Z ,L.4

-X ( n ) f __: j'X c.l.\ R 4 \ ( Ri. - J C.1. )( R3) ::::. f( I \ \"')~ ' X ' ) ~" J C'.'\

( ~19-~ - ~ Xc."l-~ 3) (R- j X e_~ ') =- - j Xc.y~, R"' "\

~l.~~ ~'1 - ~ X C.'2. K~ R" - ~ Xe.'-\~ '2. \{~ - Xc..4 Xc..1 ~ 3 = -j X~~ ~, R~

~· ~3 ~ l\ - Xc.~X. u ~31 -j l Xc.8 ,3 R'I .,,. X ... s ... ~31 = - ~ X '-'\~ I~ '\

Xc).~ ~R'i -t x~ Q.,~ = x'-'< '<, ~~

t<-i ~~ '<-z. '<3 - ~'~" G -t -wc"l... W C t.t we.\{

~1. ~"

\ \ = -we'\ wc'2.. R~~~ ~-z..~l ~,\<.~ 1" -

c'1.- ~ c \\

= "Q'" \<" C \\ e,1.. (0'2... - Co.M.-N:1 \ ~e.~c.(L w j,.C) ~

w -- j ~LR;C,.C,_

~ \ f't'\~eK\~J Co"" f ooe.--\-

l= \ \

LI\ ~,.R'1c"\c'2.

Question (7) The ac bridge circuit of Figure 7 is known as a Maxwell bridge and is used for accurate measurement

of inductance and resistance of a coil in terms of a standard capacitance Cs. Find an expression for Rx

and Lx when the bridge is balanced.

LJ-z .- _- j Xc.s R

I -

R- ''x J c~

7 - ~.., '-l... - ....

23 - ~~ Lx

~\',J~ \:}~~ ·= 0

"3"s Lz

Figure 7

J

z. / 3

z; 7_ x ;- Z2. 7_~ - L.7. L.3 t- L'l.L~ ./"'

Z2. -Z.3

\ -j )(C5-« ]

l R- J X c_~

R2R3 ( R -j X~ )

- j Xc.s R

-Zx ~\<L ~1

_ - - ~ ~; ~1.~~ - -t"

-~ A<-s~ _ - ~~~Q.

'Zx ~,. \< 1 . 1<z. R~

- --t- J R xcs

. ;- j

A.x -

G{(L>< = \<,_ ?.~ e,,6cs

\ Lx = ~LR3 Cs \