Page 298 - Handbook of Electrical Engineering

284 HANDBOOK OF ELECTRICAL ENGINEERING

Table 11.4. Values of time corresponding to the currents in Table 11.3

X-to-R ratio T 1 (sec) T 2 (sec) T 3 (sec) T 4 (sec) T 5 (sec) T 6 (sec)
500.0000 .010000 .02002 .03000 .04002 .0500 .0600
100.0000 .010000 .02006 .03000 .04006 .0500 .0601
50.0000 .010000 .02012 .03002 .04012 .0500 .0601
30.0000 .010020 .02020 .03002 .04018 .0500 .0602
25.0000 .010020 .02022 .03004 .04020 .0501 .0602
20.0000 .010040 .02028 .03006 .04024 .0501 .0602
16.0000 .010040 .02034 .03008 .04028 .0501 .0603
14.0000 .010060 .02038 .03012 .04032 .0502 .0603
12.0000 .010080 .02042 .03014 .04036 .0502 .0603
10.0000 .010140 .02048 .03020 .04040 .0503 .0604
8.0000 .010220 .02058 .03028 .04048 .0503 .0604
6.0000 .010300 .02070 .03042 .04058 .0505 .0605
5.0000 .010440 .02080 .03054 .04068 .0506 .0606
4.0000 .010000 .02092 .03072 .04082 .0508 .0608
3.0000 .010700 .02114 .03098 .04104 .0510 .0610
2.0000 .011240 .02152 .03146 .04148 .0515 .0615
1.0000 .012460 .02250 .03250 .04250 .0525 .0625
0.5000 .013520 .02352 .03352 .04352 .0535 .0635
0.2000 .014380 .02438 .03438 .04438 .0544 .0644
0.1000 .014680 .02468 .03468 .04468 .0547 .0647

Notes:
a) I 1 , I 3 and I 5 are the maximum or upper peak values at times T 1 , T 3 and T 5 .
b) I 2 , I 4 and I 6 are the minimum or lower peak values at times T 2 , T 4 and T 6 .
c) If the supply frequency is 60 Hz then multiply the times by the ratio of 50:60.

The worst case is where the resistance is zero. The current i response is,

V ˆ π π
i = − sin θ − + sin ωt +θ −
ωL 2 2
V ˆ
= (cos θ − cos(ωt + θ))
ωL

With θ = 0 this current becomes
V ˆ
i = (1 − cos ωt)
ωL

The sinusoidal term in the brackets oscillates between zero and +2.0. This term is called the
‘doubling factor’ when the time is t = π/ω has the value of 2.0.
The bad cases occur when the resistance is small, see Figure 11.8.

The response is then,
V ˆ −Rt
i = e L − cos ωt (11.6)
Z