Q1 - a (15 points) Exam2-Solution.pdf · Q1 - a (15 points) Write the mesh equations for i1, i2, i3, and i4 in the matrix form (Note: Don’t solve for the mesh currents i1, i2, i3,

Q1 - a (15 points)

Write the mesh equations for i1, i2, i3, and i4 in the matrix form

(Note: Don’t solve for the mesh currents i1, i2, i3, and i4)

Solution

From the super-mesh

2i1 + 8(i1-i4) + 3(i3-i4) + 4(i3-i2) = 0

10i1 - 4i2 + 7i3 - 11i4 = 0 ----(1)

i1 – i3 = 2 ----- (2)

Mesh-2

-20 + 5i2 + 4(i2-i3) = 0

9i2 + -4i3 = 20 ----(3)

Mesh-4

-10 + 3(i4-i3) + 8(i4 – i1) = 0

-8i1 - 3i3 + 11i4 = 10 ----(4)

Q1 – b (15points)

Given that

i3 = 0.5 A i4 = -2 A

a) Solve for i1 and i2

b) Calculate the branch currents (ia and ib) c) Calculate the voltages (Vc and Vd)

d) Calculate the power delivered by the 3 A current source.

Solution

a)

i1 = 3 A

i2= -2 A

b)

ia= i3-i4 = 0.5 +2 = 2.5 A

ib= id+2 = (i2-i3)+2 = (-2-0.5)+2 = -0.5 A

c)

Vc = -10 ( i2 )= -10 ( -2) = 20 V

Vd= 5 (i2 – i3) = 5(-2-0.5) = -12.5 V

d)

V15Ω = 15(i1-i3) = 15(3-0.5) = 15(2.5) = 37.5 V )

P3A = -(3)(37.5) = - 112.5 W

Q2 (20)

+ −

2 xi

+−

2 Ω

3 Ωxi

10 V

a

b

For the circuit shown above , find the followings :

(a) The open circuit voltage between terminals a and b ?

(b) The short circuit current through the terminals a and b ?

(c) The Thevenin equivalent resistant between terminals a and b ?

(d) The load resistant RL between terminals a and b that will absorb the maximum power ? (e) The maximum power absorbed by the load resistant RL in part (d) ?

Solution

+ −

2 xi

+−

2 Ω

3 Ωxi

10 V

a

b

OCV

+

− OC OC

10 5 0 2

3 2 V 0 V 2 V

x x

x x

i i A

i i

− + = ⇒ =

− + + = ⇒ =

KVL on loop 1

KVL on loop 2

0 A( ) a (6)

+ −

2 xi

+−

2 Ω

3 Ωxi

10 V

a

b

3V 3 2 0 x x xi i iΩ = = ⇒ =

scI3V Ω

+

− sc10

I I 5 2

A= = =I

( ) b (6)

OC

SC

TH

(c)

V 2R

I 5= = Ω

L TH

(d)

2R R

5= = Ω

2oc

maxTH

(d)

V 4 5P = 2.5 W

4R 4(2 /5) 2= = =

Q3 (25)

Part I For the RC circuit shown below , the voltage across the capacitor and the current through the capacitor are

RC (t)

v+

−

(t)i

10tv(t) = 35e V for t > 0

−

10ti(t) = 7e mA for t > 0

−

Circle the correct answer :

(a) The value of the resistor R is

1 1(i) 7 k (ii) 200 k (iii) 35 k (iv) 5 k (v) k (vi) k5 200

Ω Ω Ω Ω Ω Ω

(a) The value of the capacitor C is

(i) 2000 µF (ii) 250 µF (iii) 200 µF (iv) 20 µF (v) 10 µF (vi) 5 µF

Part II The equivalent capacitance between terminals a and b in the

circuit shown below is 8 µF .

a

b

(c) The value of the capacitor C is (Circle the correct answer ) (i) 6 µF (ii) 5 µF (iii) 8 µF (iv) 2 µF (v) 10 µF (vi) 4 µF

Part III The voltage v(t) across a 2 mF capacitor is shown below

16

0 1 2 3 4t

v(t)

(d) Plot current i(t) through the capacitor showing all significant values ?

i(t) mA

t0 1 2

3 4

5

32

32