ABSTRACT
Considering the RC network shown in Figure 5.1, we can use Kirchhoff’s current law (KCL) to write Equation (5.1).
(5.1)
i.e.,
If Vm is the initial voltage across the capacitor, then the solution to Equation (5.1) is
(5.2)
where CR is the time constant. Equation (5.2) represents the voltage across a discharging capacitor. To
obtain the voltage across a charging capacitor, let us consider Figure 5.2. Using KCL, we get
(5.3)
If the capacitor is initially uncharged, that is, v0(t) = 0 at t = 0, the solution to Equation (5.3) is given as
(5.4)
C
dv t dt
v t R
o o( ) ( )+ = 0
dv t dt
v t CR
o o( ) ( )+ = 0
v t V em
0( ) = -
C
dv t dt
v t V R
o o s( ) ( )+ -
= 0
v t V eS
0 1( ) = - Ê
Ë ÁÁ
ˆ
¯ ˜˜
Example 5.1 and Example 5.2 illustrate the use of MATLAB for solving problems related to RC network.
