Transcript Chapter-6

L
 v 
i
L
 v 
i
di
v=L
dt
dv
i =C
dt
t

1
i(t ) =
v d   i(t 0 )
L
t0
1
w = Li 2
2
di
p = Li
dt
v(t ) =
1
C
t

i d   v (t 0 )
t0
1 2
w = Cv
2
dv
p = Cv
dt
Inductors in Series
1 1
1
  
Lequ  L1 L 2
1 


Ln 
Therefore inductor combine like resistor
5.1.1 Capacitors in Series
5.1.1 Capacitors in Parallel
Therefore capacitor combine like conductor
Example 5.1
A voltage source is applied to a 5-F capacitor as
shown.
Sketch the capacitor current and the stored energy as a
function of time.
dv t 
i t   C
dt
dv t 
5
dt
1
2
w t   C v t 
2
1
  5v s2 t 
2
Example 5.2
A current source is applied to a 5-F capacitor.
Sketch the capacitor voltage as a function of time.
t
1
v t    i s  d
5 
The capacitor voltage is related to
area Under current source.
For example area at t = 1 s is
Area of Triangle is (1)(10)=10
V(1s)=10/5= 2V.
For example area at t=3 s is
10+10+5 = 25 hence
V(3s)=25/5= 5V.
Example 5.3
A current source is applied to a 5-H inductor as shown. Sketch
the voltage across the inductor versus time.
di t 
v t   L
dt
1 2
w t   Li t 
2
Example 5.4
A voltage source is applied to a 5-H inductor as
shown. Sketch the inductor current versus time.
1
i t  
L
t
 v  d 

1
i t  
L
t
 v  d 
