136 Practical MATLAB® Applications for Engineers
ANALYTICAL SolutionThe set of loop differential equations are
Loop#1:( 12 )^11212222
()
( ) () ()
()
LL
di t
dt
RRit RitL
di t
dt
0Loop#2:
()
() ( )
()
L ()()
di t
dt
Ri t L L
di t
dt
2 1 21 2 3 2 RRit 232 ^0The set of initial (or boundary) current conditions such as i 1 (t 0 ) = I 1 and i 2 (t 0 ) = I 2
must be known to completely specify its response.
R.2.119 Recall that capacitors and inductors can be combined and represented by a single
equivalent element depending on the type of connection (series or parallel).
The voltage and current divider rules for capacitors and inductors are stated
below.
R.2.120 The voltage divider rule is used to evaluate the voltage drops VL1 and VL 2
across the inductors L 1 and L 2 when connected in series with and applied volt-
age Vo across them as shown in Figure 2.34.
VL
L
LL
1 1 V
12 oVL
L
LL
2 2 V
12 oR.2.121 Let us now consider two inductors L 1 and L 2 connected in parallel, with a current
(source) Io feeding the parallel combination as indicated in Figure 2.35.
FIGURE 2.34
Voltage divider rule across inductors in series of R.2.120.
L 1L 2Vo++
−− +−VL 1VL 2