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Консультация № 149704
06.11.2008, 21:00
0.00 руб.
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1
Помогите решить задачу. Дано: I=10 А, U=100 В, z=R+jx, R=(1/4)z 
Обсуждение
08.11.2008, 03:17
общий
это ответ
Здравствуйте, Snegovik!
Исходные данные указаны, вроде бы, "с хитростью", но на самом так, чтобы облегчить расчёты тому, кто "соображает", что и сделаем. Ток I = 10 А распределяется между двумя параллельными ветвями с одинаковыми комплексными сопротивлениями Z, след-но, по каждой ветви протекает I[sub]в[/sub] = 10/2 = 5 А (обе ветви подключены к одному и тому же напряжению, сдвиг по фазе м-ду напряжением и током одинаков, значит, оба тока совпадают по фазе, и их комплексная сумма равна арифметической сумме). Модуль Z = U/I[sub]в[/sub] = 100/5 = 20 Ом, а R = (1/4)*Z = (1/4)*20 = 5 Ом. Мощность, выделяемая в ветви с ваттметром, и, след-но, показания ваттметра P = I[sub]в[/sub][sup]2[/sup]*R = 5[sup]2[/sup]*5 = 125 Вт. Активная составляющая тока ветви I[sub]ав[/sub] = I[sub]в[/sub]*COS([$966$]) = P/U = 125/100 = 1.25 А; COS([$966$]) = I[sub]ав[/sub]/I[sub]в[/sub] = 1.25/5 = 0.25, откуда SIN([$966$]) = [size=4][$8730$]([/size]1 - [size=3]([/size]COS([$966$])[size=3])[/size][sup]2[/sup][size=4])[/size] = [size=4][$8730$][/size](1 - 0.25[sup]2[/sup]) = 0.9682. Реактивная составляющая тока ветви I[sub]рв[/sub] = I[sub]в[/sub]*SIN([$966$]) = 5*0.9682 = 4.841 А. X = Z*SIN([$966$]) = 20*0.9682 =19.365 Ом.
Исходные данные указаны, вроде бы, "с хитростью", но на самом так, чтобы облегчить расчёты тому, кто "соображает", что и сделаем. Ток I = 10 А распределяется между двумя параллельными ветвями с одинаковыми комплексными сопротивлениями Z, след-но, по каждой ветви протекает I[sub]в[/sub] = 10/2 = 5 А (обе ветви подключены к одному и тому же напряжению, сдвиг по фазе м-ду напряжением и током одинаков, значит, оба тока совпадают по фазе, и их комплексная сумма равна арифметической сумме). Модуль Z = U/I[sub]в[/sub] = 100/5 = 20 Ом, а R = (1/4)*Z = (1/4)*20 = 5 Ом. Мощность, выделяемая в ветви с ваттметром, и, след-но, показания ваттметра P = I[sub]в[/sub][sup]2[/sup]*R = 5[sup]2[/sup]*5 = 125 Вт. Активная составляющая тока ветви I[sub]ав[/sub] = I[sub]в[/sub]*COS([$966$]) = P/U = 125/100 = 1.25 А; COS([$966$]) = I[sub]ав[/sub]/I[sub]в[/sub] = 1.25/5 = 0.25, откуда SIN([$966$]) = [size=4][$8730$]([/size]1 - [size=3]([/size]COS([$966$])[size=3])[/size][sup]2[/sup][size=4])[/size] = [size=4][$8730$][/size](1 - 0.25[sup]2[/sup]) = 0.9682. Реактивная составляющая тока ветви I[sub]рв[/sub] = I[sub]в[/sub]*SIN([$966$]) = 5*0.9682 = 4.841 А. X = Z*SIN([$966$]) = 20*0.9682 =19.365 Ом.
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