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Консультация № 195136
06.04.2019, 12:39
0.00 руб.
1
1
1
Здравствуйте! Прошу помощи в следующем вопросе:
364 ЭДС батареи 100 В, сопротивление R1 = 100 Ом, R2= 200 Ом и R3= 300 Ом, сопротивление вольтметра 2 кОм. Какую разность потенциалов показывает вольтметр?
[80 В]
364 ЭДС батареи 100 В, сопротивление R1 = 100 Ом, R2= 200 Ом и R3= 300 Ом, сопротивление вольтметра 2 кОм. Какую разность потенциалов показывает вольтметр?
[80 В]
Прикрепленные файлы:
Обсуждение
07.04.2019, 14:46
общий
это ответ
Здравствуйте, kuznarskaavalentina!
Ток I1 от источника напряжения E создаёт на резисторе R1 некоторое падение напряжения U1 = I1 · R1
Изза потерь энергии на резисторе R1, Вольтметр получит не всё напряжение ЭДС E , а лишь часть его : Uv = E - U1
Ток I1 = Iv + I2 разветвляется на 2 ветви :
ток Iv = Uv / Rv (тут Rv = 2 кОм - сопротивление вольтметра, эти величины связаны Законом Ома)
и ток I2 = Uv / R23 . Тут R23 = R2 + R3 = 200 + 300 = 500 Ом .
Во 2м уравнении заменяем ненужное нам U1 на его выражение из первого и 3го уравнений :
Uv = E - (Iv + I2) · R1
А в нём затем заменяем токи Iv и I2 на их выражения из ниже-уравнений.
Получаем Uv = E - (Uv / Rv + Uv / R23) · R1
Осталось решить это уравнение с одним неизвестным :
E1/R1 - Uv/R1 = Uv / Rv + Uv / R23
E1/R1 = Uv · (1/R1 + 1/Rv + 1/R23)
Uv = E / (R1 · (1/R1 + 1/Rv + 1/R23)) = E / (R1/R1 + R1/Rv + R1/R23) =
=100 / (1 + 100/2000 + 100/500) = 100 / (1+0,05+0,2) = 100 / 1,25 = 80 Вольт
Ток I1 от источника напряжения E создаёт на резисторе R1 некоторое падение напряжения U1 = I1 · R1
Изза потерь энергии на резисторе R1, Вольтметр получит не всё напряжение ЭДС E , а лишь часть его : Uv = E - U1
Ток I1 = Iv + I2 разветвляется на 2 ветви :
ток Iv = Uv / Rv (тут Rv = 2 кОм - сопротивление вольтметра, эти величины связаны Законом Ома)
и ток I2 = Uv / R23 . Тут R23 = R2 + R3 = 200 + 300 = 500 Ом .
Во 2м уравнении заменяем ненужное нам U1 на его выражение из первого и 3го уравнений :
Uv = E - (Iv + I2) · R1
А в нём затем заменяем токи Iv и I2 на их выражения из ниже-уравнений.
Получаем Uv = E - (Uv / Rv + Uv / R23) · R1
Осталось решить это уравнение с одним неизвестным :
E1/R1 - Uv/R1 = Uv / Rv + Uv / R23
E1/R1 = Uv · (1/R1 + 1/Rv + 1/R23)
Uv = E / (R1 · (1/R1 + 1/Rv + 1/R23)) = E / (R1/R1 + R1/Rv + R1/R23) =
=100 / (1 + 100/2000 + 100/500) = 100 / (1+0,05+0,2) = 100 / 1,25 = 80 Вольт
5
Все очень понятно изложено, спасибо большое за помощь
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