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Homework 4 Solution - Circuits and Electronics | ECE 3710, Assignments of Electrical and Electronics Engineering

Georgia Institute of Technology - Main CampusElectrical and Electronics Engineering

Material Type: Assignment; Class: Circuits & Electronics; Subject: Electrical & Computer Engr; University: Georgia Institute of Technology-Main Campus; Term: Unknown 1989;

Typology: Assignments

Pre 2010

Uploaded on 08/05/2009

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koofers-user-qg3 🇺🇸

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ECE 3710 D Summer 2007
Homework 4 Solution
P3.11
( ) ( )
( )
∫
+=
t
vdtti
C
t
v
0
0
1
( ) ( )
∫
×=
t
dttit
v
0
6
102
(
)
(
)
(
)
t
i
t
v
t
p
=
( ) ( )
tCvtw
2
1
=
(
)
t
v
26
10
25
.
××=
−
P3.45
H
=
L
( )
(
)
dt
t
di
Lt
v
L
L
=
(
)
(
)
(
)
t
i
t
v
t
p
LL
=
pf3

Partial preview of the text

Download Homework 4 Solution - Circuits and Electronics | ECE 3710 and more Assignments Electrical and Electronics Engineering in PDF only on Docsity!

ECE 3710 D Summer 2007

Homework 4 Solution

P3.11 ( ) = ∫ ( ) + ( )

t itdt v C

vt 0

( ) = × ∫ ( )

t vt itdt 0

p ( t ) =v(t )i ( t )

w ( )t Cv^2 ( ) t

= 0. 25 × 10 −^6 × v 2 (t )

P3.45 L= 2 H

dt

di t

vL t = L^ L

p ( t ) = vL(t )i L( t )

( ) [ ( )]^2

wt = Li L t

P4.1 The time constant τ is the interval required for the voltage to fall to exp(-1) ≅ 0.368 times its initial value. The time constant is given by

τ = RC. Thus to attain a long time constant, we need large values for both R

and C.

P4.7 (a)

(b)

[ ( )]

2500 exp( 100 ) W

2

t μ

R

v t

pR t =^ R = −

(c)

(d) The initial energy stored in the capacitance is

[ ( )]

25 J

6 2

2

= μ

= × × ×

−

W Cv C

P4.30 The time constant τ is the interval required for the current to fall to exp(-1) ≅ 0.368 times its initial value. The time constant is given by

τ = L/ R. Thus to attain a long time constant, we need a large value for L

and a small value for R.

50 exp ( 0. 02 ) 50 exp( 50 ) for 0

0 for 0

50 exp 0. 02 50 exp 50 for 0

v 50 for 0

20 ms

C

t t t

v t t

t t t

t t

RC

R

25 J

25 exp 100

2500 exp 100

0

0

0

= μ

∞

∞

∞

t

tdt

W pRtdt