Page 846 - Mechanical Engineers' Handbook (Volume 2)

1 Basic Analog Electronics 837

Time response
V
– + i(t)
t = 0
V

R
R i L
t
Figure 20 An RL circuit (see Eq. 18b).

V Time response
– +
t = 0 i(t)
V
R i L R
t
Figure 21 An RL circuit (see Eq. 19b).

a. Differential equation:
V dv
C I (21a)
R dt
Solution:

v RI(1 e t / T ) (see Fig. 22) (21b)
b. Differential equation:

V dv
C 0 (22a)
R dt
Solution:
v RIe t / T (see Fig. 23) (22b)

The resulting observations from these circuits are that the voltage does not change
instantly across a capacitor, but the current can change instantly. Also, the voltage can change
instantly across an inductor, but the current cannot change instantly:

t = 0 Time response
(t)
+
R • C I IR
–
t
Figure 22 An RC circuit (see Eq. 21b).