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Консультация № 174880
05.12.2009, 03:31
0.00 руб.
05.12.2009, 07:53
0
1
1
Здравствуйте, уважаемые знатоки. Помогите с решением задачи.
Условие:
Рассчитайте удельное объемное сопротивление материала, если образец из него диаметром 50 мм и толщиной 2 мм при частоте 500 Гц имеет tgб=0.01 и емкость С=200пФ. Поверхностной утечкой пренебрегите.
Заранее спасибо.
Условие:
Рассчитайте удельное объемное сопротивление материала, если образец из него диаметром 50 мм и толщиной 2 мм при частоте 500 Гц имеет tgб=0.01 и емкость С=200пФ. Поверхностной утечкой пренебрегите.
Заранее спасибо.
Обсуждение
08.12.2009, 05:31
общий
это ответ
Здравствуйте, Greennitro.
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 = 500 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*500*200*10-12*0.01) ≈ 1.6*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 = 500 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*500*200*10-12*0.01) ≈ 1.6*108 ом*м.
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