Page 845 - Mechanical Engineers' Handbook (Volume 2)

836 Mechatronics

A y(t)

0.368A

T
T
= time constant
= time to decay to 36.8% of original time
Figure 18 First-order response.

Consider the following circuits and the resulting equations, solutions, and time responses
to step inputs:
1. RL circuits:
L
T (17)
R
a. Differential equation:
di
Ri L V (18a)
dt
Solution:
V
i (1 e t / T ) (see Fig. 20) (18b)
R
b. Differential equation:
di
Ri L 0 (19a)
dt
Solution:
V
i (1 e t / T ) (see Fig. 21) (19b)
R
2. RC circuits:
T RC (20)

y(t)
A

0.632A

T
T = time to rise to 63.2% of final value
Figure 19 First-order response.