PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Direct Current and Transient Analysis 129

following fi rst-order linear differential equation is obtained in terms of the

unknown loop current i(t) illustrated as follows:

1

C

∫itdt Rit() 
() V

then

it

V

R

()
 et/

where τ = RC.

vt VeR t

()
t/ for 0

and

vt V vt V VeCR t

()

() t/ for 0

R.2.99 When a sudden DC voltage V is applied to a simple series RC circuit (with vc(0) =

0 V), the capacitor voltage charges up to

vC(t) = V (1 − e−t/)

and the current through C is then given by

iCt t

V

R

()
 e/

where τ = RC (s) is the time constant of the circuit.

R.2.100 A charged capacitor in an RC circuit with an initial voltage V(0) and no sources,

as indicated in Figure 2.29, discharges with the following current and voltage

relations:

vt VoeC

()
 t/

FIGURE 2.28

RC series circuit.

V

R

C

Switch closes at t = 0

i(t)