PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

128 Practical MATLAB® Applications for Engineers

solving for i(t) results in

it

V

R

et

L

R

()

( 1  t/τ) for 0 with 

R.2.96 When a sudden voltage V is applied to a simple-series RL circuit, a transient con-
dition results (recall that the inductor controls the current fl ow), and the general
current and voltage relations are given by

it

V

R

()
 () 1 et/

and the voltage across the resistor R is given by

vt VR e
()
( 1  t/)

and the voltage across the inductor L is given by

vt V vt V V VeLR Ve
()

 () ( tt//)

where τ = L/R (s) is the time constant of the circuit. Note that V = vR(t) + vL(t).

R.2.97 In an RL circuit in which the inductor is charged and its initial current is Io and
initial voltage across Vo (with no source), the inductor discharges and the current
and voltage relations are given by

it I e

V

R

()

o**tt//o e

and

vt V eL
() t

• 
  

/

o



R.2.98 Let us now turn our attention to the RC series circuit shown in Figure 2.28.
The switch is open for t < 0, and closes at t = 0, assuming that the capaci-
tor is discharged, that is, vC(0) = 0. Then applying KVL (around the loop), the

FIGURE 2.27
RL series circuit.

V

R

L

Switch closes at t = 0

i(t)