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Консультация № 200427
16.03.2021, 10:46
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Здравствуйте! У меня возникли сложности с таким вопросом:
Колебательный контур состоит из конденсатора емкостью 7 мкФ, катушки с индуктивностью 0,23 Гн и сопротивлением 40 Ом.
6) Каков период колебаний в контуре?
7) На какую длину волны настроен контур?
Колебательный контур состоит из конденсатора емкостью 7 мкФ, катушки с индуктивностью 0,23 Гн и сопротивлением 40 Ом.
6) Каков период колебаний в контуре?
7) На какую длину волны настроен контур?
Обсуждение
17.03.2021, 11:47
общий
это ответ
Здравствуйте, gleb.babin!
Предлагаю Вам следующее решение задачи.
Дано: C=7 мкФ=7*10-6 Ф -- ёмкость конденсатора, L=0,23 Гн -- индуктивность катушки; R=40 Ом -- активное сопротивление катушки.
Определить: T -- период колебаний в контуре; [$955$] -- длину волны, на которую настроен контур.
В соответствии с известными формулами [1, с. 398 - 401], имеем
-- собственная частота колебательного контура;
-- коэффициент затухания колебаний в контуре.
Поскольку [$948$]2<<[$969$]02, постольку затухание невелико и
-- собственная частота затухающих колебаний в контуре;
-- период затухающих колебаний в контуре;
-- длина волны, на которую настроен контур.
Ответ: T=7,97*10-3 с; [$955$]=2,4*106 м.
Литература
1. Кухлинг Х. Справочник по физике. -- М.: Мир, 1982. -- 520 с.
Предлагаю Вам следующее решение задачи.
Дано: C=7 мкФ=7*10-6 Ф -- ёмкость конденсатора, L=0,23 Гн -- индуктивность катушки; R=40 Ом -- активное сопротивление катушки.
Определить: T -- период колебаний в контуре; [$955$] -- длину волны, на которую настроен контур.
Решение
В соответствии с известными формулами [1, с. 398 - 401], имеем
[$969$]0=1/[$8730$](LC)=1/[$8730$](0,23*7*10-6)[$8776$]788 (с-1)
-- собственная частота колебательного контура;
[$948$]=R/(2L)=40/(2*0,23)[$8776$]87,0 (с-1)
-- коэффициент затухания колебаний в контуре.
Поскольку [$948$]2<<[$969$]02, постольку затухание невелико и
[$969$]=[$8730$]([$969$]02-[$948$]2)[$8776$][$969$]0=778 (c-1)
-- собственная частота затухающих колебаний в контуре;
T=2[$960$]/[$969$]=2[$960$]/788[$8776$]7,97*10-3 (с)
-- период затухающих колебаний в контуре;
[$955$]=сT[$8776$]3,00*108*7,97*10-3[$8776$]2,4*106 (м)
-- длина волны, на которую настроен контур.
Ответ: T=7,97*10-3 с; [$955$]=2,4*106 м.
Литература
1. Кухлинг Х. Справочник по физике. -- М.: Мир, 1982. -- 520 с.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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