Vs 2 0 V R 1 4 0 R 1 4 0 , OmegaR 1 4 0 R 2 9 0 R 2 9 0 , OmegaR 2 9 0 R 3 9 0 R 3 9 0 , OmegaR 3 9 0 Which KCL equation correctly describes the relationship between nodal voltage VaV aVa and source voltage VsV sVs Then, solve the equation for VaV aVa ( a ) ( R 1 R 2 R 3 ) Va VsR 1 ( R 1 R 2 R 3 ) times V a frac V s R 1 ( R 1 R 2 R 3 ) Va R 1 Vs ( b ) ( 1 R 1 1 R 2 1 R 3 ) Va VsR 1 left ( frac 1 R 1 frac 1 R 2 frac 1 R 3 right ) times V a frac V s R 1 ( R 1 1 R 2 1 R 3 1 ) Va R 1 Vs ( c ) ( 1 R 1 1 R 2 1 R 3 ) Va VsR 1 left ( frac 1 R 1 frac 1 R 2 frac 1 R 3 right ) times V a frac V s R 1 ( R 1 1 R 2 1 R 3 1 ) Va R 1 Vs ( d ) ( R 1 R 2 R 3 ) Va VsR 1 ( R 1 R 2 R 3 ) times V a frac V s R 1 ( R 1 R 2 R 3 ) Va R 1 Vs ( e ) ( 1 R 1 1 R 2 1 R 3 ) Va VsR 1 left ( frac 1 R 1 frac 1 R 2 frac 1 R 3 right ) times V a frac V s R 1 ( R 1 1 R 2 1 R 3 1 ) Va R 1 Vs Va V a Va VVV

The Answer is in the image, click to view ...

Question: Vs = 2 0 V R 1 = 4 0 R _ 1 = 4 0 , OmegaR 1 = 4 0 R

= 20

1 = 40

_1 = 40 \, \

OmegaR

1 = 40

2 = 90

_2 = 90 \, \

OmegaR

2 = 90

3 = 90

_3 = 90 \, \

OmegaR

3 = 90

Which KCL equation correctly describes the relationship between nodal voltage VaV

_

aVa

and source voltage VsV

_

sVs

?

Then, solve the equation for VaV

_

aVa

.

(

) (

1

2

3)

=

VsR

1 (

_1 -

_2 -

_3) \

times V

_

= \

frac

{

_

} {

_1} (

1

2

3)

=

1

(

) (1

1 + 1

2 + 1

3)

=

VsR

1 \

left

(- \

frac

{1} {

_1} + \

frac

{1} {

_2} + \

frac

{1} {

_3} \

right

) \

times V

_

= \

frac

{

_

} {

_1} (

1 1 +

2 1 +

3 1)

=

1

(

) (1

1 + 1

2 + 1

3)

=

VsR

1 \

left

(\

frac

{1} {

_1} + \

frac

{1} {

_2} + \

frac

{1} {

_3} \

right

) \

times V

_

= \

frac

{

_

} {

_1} (

1 1 +

2 1 +

3 1)

=

1

(

) (

1 +

2 +

3)

=

VsR

1 (

_1 +

_2 +

_3) \

times V

_

= \

frac

{

_

} {

_1} (

1 +

2 +

3)

=

1

(

) (1

1 + 1

2 1

3)

=

VsR

1 \

left

(\

frac

{1} {

_1} + \

frac

{1} {

_2} - \

frac

{1} {

_3} \

right

) \

times V

_

= \

frac

{

_

} {

_1} (

1 1 +

2 1

3 1)

=

1

=

_

=

=________

VVV

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