Instantaneous Values of Sine Waves (MA194E)

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Written by: Newton C. Braga

Instantaneous Values of Sine Waves (MA194E)

The instantenous value for a sine wave depends on the time on the cycle according the next formula:

Formula:

V = Vp x ( Tv / 100 )

 

Where:

V is the instantaneous value (voltage, for instance)

Vp is the peak value (voltage, for instance)

Tv is the value found in the next table for the desired phase angle

Phase Angle (degrees) Percent (Tv)
0 180 180 360 0,000000
1 179 181 359 1,745241
2 178 182 358 3,489950
3 177 183 357 5,233596
4 176 184 356 6,975647
5 175 185 355 8,715574
6 174 186 354 10,45285
7 173 187 353 12,18693
8 172 188 352 14,92731
9 171 189 351 15,64345
10 170 190 350 17,36482
11 169 191 349 19,08090
12 168 192 348 20,79117
13 167 193 347 22,49511
14 166 194 346 24,19219
15 165 195 345 25,88190
16 164 196 344 27,56374
17 163 197 343 29,23717
18 162 198 342 30,90170
19 161 199 341 32,55682
20 160 200 340 34,20201
21 159 201 339 35,83680
22 158 202 338 37,46066
23 157 203 337 39,07311
24 156 204 336 40,67366
25 155 205 335 42,26183
26 154 206 334 43,83711
27 153 207 333 45,39905
28 152 208 332 46,94715
29 151 209 331 48,48096
30 150 210 330 50,00000
31 149 211 329 51,50381
32 148 212 328 52,99192
33 147 213 327 54,46391
34 146 214 326 55,91929
35 145 215 325 57,35764
36 144 216 324 58,77853
37 143 217 323 60,18150
38 142 218 322 61,56615
39 141 219 321 62,93204
40 140 220 320 64,27876
41 139 221 319 65,60590
42 138 222 318 66,91306
43 137 223 317 68,19984
44 136 224 316 69,46584
45 135 225 315 70,71068
46 134 226 314 71,93398
47 133 227 313 73,13537
48 132 228 312 74,31448
49 131 229 311 75,47095
50 130 230 310 76,31448
51 129 231 309 77,71460
52 128 232 308 78,80107
53 127 233 307 79,86355
54 126 234 306 80,90170
55 125 235 305 81,91521
56 124 236 304 82,90376
57 123 237 303 83,86706
58 122 238 302 84,80481
59 121 239 301 85,71673
60 120 240 300 86,60254
61 119 241 299 87,46198
62 118 242 298 88,29475
63 117 243 297 89,10065
64 116 244 296 89,87940
65 115 245 295 90,63078
66 114 246 294 91,35455
67 113 247 293 92,05048
68 112 248 292 92,71838
69 111 249 291 93,35804
70 110 250 290 93,96926
71 109 251 289 94,55186
72 108 252 288 95,10565
73 107 253 287 95,63048
74 106 254 286 96,12617
75 105 255 285 96,59258
76 104 256 284 97,02957
77 103 257 283 97,43700
78 102 258 282 97,81476
79 101 259 281 98,16272
80 100 260 280 98,48077
81 99 261 279 98,76884
82 98 262 278 99,02681
83 97 263 277 99,25462
84 96 264 276 99,45219
85 95 265 275 99,61497
86 94 266 274 99,75640
87 93 267 273 99,86295
88 92 268 272 99,93908
89 91 269 271 99,98477
90 90 270 270 100,0000

 

 

Application Example:

Determine the instantaneous value of a 300 V (peak) voltage at the phase angle of 32 degrees.

Given:

Vpeak = 300 V

Cx = 32o

 

Using the formula:

V = Vpeak x Tv/100

 

Where:

Tv = value found in the table

V = 300 x 52;99/158,97 V