Unit – 3 | unit 3 graph theory - Goseeko

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Network Theory

Unit – 3

Graph theory

Q1) Find total possible no. Of trees

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A1)

T = n (n-2)

n = no. Of nodes

T = 6 (6-2) = 6 4

Q2)

Find out overall transmission parameter?

A2)

Q3)

Find overall Y-parameter?

A3)

Q4)

A4)

V1 – I1R – V2 = 0

V1 – V2 = I1R

I1 = V1 - V2

V2 = I2R + V1

I2 = - V1 + V2

Y11 =

Y12 = Y21 =

Y22 =

Q5)

A5)

Y-parameter does not exist as V1 = V2

Q6)

A6)

I1 = V1Ya + (V1 – V2)Yc

I1 = (Ya + Yc)V1 - YcV2

I2 = V2Yb + (V2 – V1)Yc

I1 = (Yb + Yc)V2 - YcV1

Y11 = Yb + Yc

Y12 = Y21 = - Yc

Y22 = Yb + Yc

Q7)

A7)

Q7)

Find Y-parameter?

A8)

-I1 + – 2V2 + + 2V1 = 0

I1= V1 + V1 - 3V2 + 2V1

I1= 4V1 - 3V2V

V2 + 2V2- 2V1 = 2(I2 + 2V1)

- 2V1 + 3V2 = 2(I2 + 2V1)

3V2 - 2V1 – 4V1 = 2I2

I2 = -3V1 + V2

Y11 = 4

Y12 = -3

Y21 = -3

Y22 =

Q8)

Find Z-parameter

A9)

I1 = -I2

Current dependent so Z-parameter doesn’t exist

Q9)

Find z-parameter

A10)

V1 =R (I1 + I2)

V2 = R (I1 + I2)

Z11 = Z12 = Z21 = Z22 = R

Q10)

A11)

V1 = I1Za + I1Zc + I2Zc

= (Za + Zc)I1 + ZcI2

V2 = I2Zb + I2Zc + I1Zc

= (Zb + Zc)I1 + ZcI1

Z11 = (Za + Zc)

Z12 = Zc = Z21

Z22 = (Zb + Zc)

Q11)

A12)

V1 = Za(I1 - I)

(I - I1)Za+ IZc+ Zb(I + I2) = 0

I(Za + Zb + Zc) – I1Za + I2Zb = 0

I =

V1 = ZaI1 - Za

= I1 + I2

V2 = Zb(I2 + I)

= ZbI2 + Zb

= I2 + I2

Z11 =

Z12 = Z21 =

Z22 =

Can be solved by Y-A conversion

Q12)

A13)

Z11 = I2=0

V1 - (Za + Zb) = 0

= Z11 =

Z21 = I2=0

V2 - Zb +Za = 0

=

Z12 =

Z22 =

Q13)

Find Z21 ?

A14)

Z21 = I2=0

I1/2 =

= I1

V2 = I1/2

= × I1

= I1

Z21 = I2 = 0 = I1 Ω

Q14)

A15)

+ + 2V1 = 0

2Vx – 2V1 + Vx – V2 + 2V1 = 0

3Vx = V2

Vx =

I1 = V1 +

= 3V1 – 2Vx

= 3V1 – 2

V1 =

+ 2V2 = I2

3V2 - = I2

V2 = I2

V2 = I2

V1 =

=

Z11 =

Z12 =

Z21 = 0

Z22 =