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Консультация № 172609
25.09.2009, 12:34
0.00 руб.
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Уважаемые эксперты, помогите!
На цоколе электрической лампочки написано «220 В, 100 Вт». В процессе работы из-за испарения и рассеяния металла спираль лампочки становится тоньше. Какова будет мощность лампочки, если диаметр волоска спирали уменьшится на 10%?
На цоколе электрической лампочки написано «220 В, 100 Вт». В процессе работы из-за испарения и рассеяния металла спираль лампочки становится тоньше. Какова будет мощность лампочки, если диаметр волоска спирали уменьшится на 10%?
Обсуждение
26.09.2009, 08:26
общий
это ответ
Здравствуйте, Валентина В.В..
Обозначим: d0 - начальный диаметр волоска; s0 - начальная площадь поперечного сечения волоска; ρ - удельное сопротивление металла волоска; l - длина волоска; R0 - начальное сопротивление волоска; P0 = 100 Вт - начальная мощность лампочки; U = 220 В - номинальное напряжение; d1 - конечный диаметр волоска; s1 - конечная площадь поперечного сечения волоска; R1 - конечное сопротивление волоска; P0 - искомая конечная мощность лампочки. Имеем: P0 = U2/R0 (1); P1 = U2/R1 (1а); R0 = ρ*l/s0 (2); R1 = ρ*l/s1 (2а); s0 = π*d02/4 (3); s1 = π*d12/4 (3а). Подставляя соответственно (3) в (2), (3а) в (2а), (2) в (1), (2а) в (1а) и разделив друг на друга полученные выражения для P1 и P0, после сокращений получаем: P1/P0 = (d1/d0)2 (4), откуда P1 = P0*(d1/d0)2 (4а), а т.к. по условию d1/d0 = 0.9, то P1 = P0*0.92 = 100*0.81 =81 Вт.
Обозначим: d0 - начальный диаметр волоска; s0 - начальная площадь поперечного сечения волоска; ρ - удельное сопротивление металла волоска; l - длина волоска; R0 - начальное сопротивление волоска; P0 = 100 Вт - начальная мощность лампочки; U = 220 В - номинальное напряжение; d1 - конечный диаметр волоска; s1 - конечная площадь поперечного сечения волоска; R1 - конечное сопротивление волоска; P0 - искомая конечная мощность лампочки. Имеем: P0 = U2/R0 (1); P1 = U2/R1 (1а); R0 = ρ*l/s0 (2); R1 = ρ*l/s1 (2а); s0 = π*d02/4 (3); s1 = π*d12/4 (3а). Подставляя соответственно (3) в (2), (3а) в (2а), (2) в (1), (2а) в (1а) и разделив друг на друга полученные выражения для P1 и P0, после сокращений получаем: P1/P0 = (d1/d0)2 (4), откуда P1 = P0*(d1/d0)2 (4а), а т.к. по условию d1/d0 = 0.9, то P1 = P0*0.92 = 100*0.81 =81 Вт.
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