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Консультация № 174638
28.11.2009, 16:31
0.00 руб.
30.11.2009, 22:03
0
1
1
Добрый день! Помогите, пожалуйста, с решением такой вот задачи: Рассчитайте удельное объемное сопротивление материалов, если при измерении диэлектрических свойств образца материала диаметром 50мм и толщиной 2 мм при частоте 50 Гц оказалось, что tgБ=0,02 и C=200 пФ. Поверхностной утечкой пренебрегите.
Спасибо.
Спасибо.
Обсуждение
30.11.2009, 11:29
общий
это ответ
Здравствуйте, Потапов Дмитрий Михайлович.
Схема замещения такая (ввиду простоты рисунок не прилагаю): параллельно с конденсатором ёмкостью C = 200 пФ = 200*10-12 Ф соединён резистор с омическим сопротивлением R, равным эквивалентному сопротивлению образца. При этом TAN(δ) определяется как отношение активной составляющей G полной проводимости Y схемы к её реактивной составляющей B, т.е. TAN(δ) = G/B (1). Кроме того: G = 1/R = S/(ρ*d) (2), где ρ - искомое удельное объемное сопротивление материала, d = 2 мм = 2*10-3 м - толщина образца материала, S - площадь поперечного сечения образца материала, причём S = π*D2/4 (3), где D = 50 мм = 50*10-3 м - диаметр образца материала, B = 2*π*f*C (4), где f = 50 Гц - частота. Совместное решение равенств (1) - (4) относительно ρ после сокращения даёт: ρ = D2/(8*d*f*C*TAN(δ)) (5). В числах: ρ = (50*10-3)2/(8*2*10-3*50*200*10-12*0.02) ≈ 8*108 ом*м.
Схема замещения такая (ввиду простоты рисунок не прилагаю): параллельно с конденсатором ёмкостью C = 200 пФ = 200*10-12 Ф соединён резистор с омическим сопротивлением R, равным эквивалентному сопротивлению образца. При этом TAN(δ) определяется как отношение активной составляющей G полной проводимости Y схемы к её реактивной составляющей B, т.е. TAN(δ) = G/B (1). Кроме того: G = 1/R = S/(ρ*d) (2), где ρ - искомое удельное объемное сопротивление материала, d = 2 мм = 2*10-3 м - толщина образца материала, S - площадь поперечного сечения образца материала, причём S = π*D2/4 (3), где D = 50 мм = 50*10-3 м - диаметр образца материала, B = 2*π*f*C (4), где f = 50 Гц - частота. Совместное решение равенств (1) - (4) относительно ρ после сокращения даёт: ρ = D2/(8*d*f*C*TAN(δ)) (5). В числах: ρ = (50*10-3)2/(8*2*10-3*50*200*10-12*0.02) ≈ 8*108 ом*м.
5
Благодарю за ответ!
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