Transcript v    di

Series-Parallel Combinations of Inductance
and Capacitance
• Inductors in Series
– All have the same current
di
v L
dt
1
1
di
v L
dt
2
2
v v v v
1
2
ECE 201 Circuit Theory I
di
v L
dt
3
3
3
1
To Determine the Equivalent Inductance
v v v v
1
2
3
di
di
di
v L
L
L
dt
dt
dt
di
v  (L  L  L )
dt
di
v L
dt
L L L L
1
2
1
2
3
3
eq
eq
1
2
3
ECE 201 Circuit Theory I
2
The Equivalent Inductance
ECE 201 Circuit Theory I
3
Inductors in Parallel
All Inductors have the same voltage across
their terminals.
ECE 201 Circuit Theory I
4
1
i 
L
1
i 
L
1
i 
L
1
 vd
t
 i (t )
1
t0
0
1
2
 vd
t
 i (t )
2
t0
0
2
3
 vd
t
 i (t )
t0
3
0
3
ECE 201 Circuit Theory I
5
i i i i
1
2
3
1 1 1
i       vd  i (t )  i (t )  i (t )
L L L 
1
i
 vd  i (t )
L
1
1 1 1
  
L
L L L
t
1
t0
1
2
0
2
0
3
0
3
t
0
t0
eq
eq
1
2
3
i (t )  i (t )  i (t )  i (t )
0
1
0
2
0
3
0
ECE 201 Circuit Theory I
6
Summary for Inductors in Parallel
ECE 201 Circuit Theory I
7
Capacitors in Series
Problem # 6.30
ECE 201 Circuit Theory I
8
Capacitors in Parallel
Problem # 6.31
ECE 201 Circuit Theory I
9