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Задать вопрос экспертам

Консультация № 199126

03.09.2020, 16:17

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Образование

Здравствуйте! Прошу помощи в следующем вопросе:
ЭДС батареи ε = 12 В, сила тока короткого замыкания I = 5 А. Какую наибольшую мощность может дать батарея во внешней цепи?
Ответ 15 Ватт
СДЕЛАТЬ РИСУНОК.

Обсуждение

давно

Студент
402651
154

03.09.2020, 17:18

общий

https://easyfizika.ru/zadachi/postoyannyj-tok/eds-batarei-akkumulyatorov-12-v-sila-toka-korotkogo-zamykaniya-5-a-kakuyu-naibolshuyu/

давно

Посетитель
226425
1567

03.09.2020, 21:59

общий

это ответ

Здравствуйте, dar777!
Дано:
ε = 12 В
I_к.з.=5А
Найти:
Р_max
Решение:
Решение будет графическим.
1. Ток короткого замыкания
I_к.з.=ε /r
r - внутреннее сопротивление источника тока.
Найдем его
r=ε /I_к.з. = 12/5 = 2,4 (Ом)
Если память не изменяет, то максимальная мощность будет при условии равенства внешнего и внутреннего сопротивлений, т.е.
при R=r.
чтоб это доказать, составим уравнение зависимости P(R)
P = I²*R
I=ε /(R+r)
Тогда
P(R)=ε ²*R/(R+r)²
P(R)=144R/(R+2.4)²
Далее возможны варианты, например, взять производную, проанализировать на экстремумы....
Но нет, мне нравятся графики

Попробуем?
Графики строить - не по морю гулять - воспользуемся подходящей программкой, хотя, если хочется, можно и по точкам, например, как в 5-м классе.
Получилось вот что

Да, по графику можно определить, что максимальная мощность 15 Вт будет выделяться на внешнем сопротивлении 2,4 Ом.
Удачи

5

Это самое лучшее решение!

Об авторе:
С уважением
shvetski

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