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Консультация № 171848
03.09.2009, 01:11
0.00 руб.
0
1
1
Уважаемые эксперты, прошу помочь.
Напряжение на концах проводника сопротивлением 5 Ом за 0,5 с равномерно возрастает от 0 до 20 В. Какой заряд проходит через проводник за это время?
Ответ и решение.
Спасибо за помощь.
Напряжение на концах проводника сопротивлением 5 Ом за 0,5 с равномерно возрастает от 0 до 20 В. Какой заряд проходит через проводник за это время?
Ответ и решение.
Спасибо за помощь.
Обсуждение
03.09.2009, 08:38
общий
это ответ
Здравствуйте, Шаврин Андрей Сергеевич.
Обозначим: i - мгновенное (текущее) значение тока в проводнике, u - мгновенное (текущее) значение напряжения на концах проводника, I - конечное значение тока в проводнике, U = 20 В - конечное значение напряжения на концах проводника, t - текущее время, T = 0.5 с - продолжительность протекания тока, R = 5 Ом - сопротивление проводника, Q - искомое значение заряда. За элементарное время dt через проводник проходит элементарный заряд dq = i*dt (1); при этом по закону Ома: i = u/R (2), откуда dq = (u/R)*dt (3). При этом, по условию, u возрастает во времени равномерно, т.е. меняется по закону u = k*t (4), где k - постоянный коэффициент. Тогда (3) приобретает вид: dq = (k/R)*t*dt (5). Проинтегрировав (5) от 0 до T, получаем: Q = (k/R)*T2/2 (6). Значение k получаем из условия: k*T = U, откуда k = U/T (7), и, подставляя в (6), окончательно: Q = (U/R)*T/2 = (20/5)*0.5/2 = 1 Кл.
Обозначим: i - мгновенное (текущее) значение тока в проводнике, u - мгновенное (текущее) значение напряжения на концах проводника, I - конечное значение тока в проводнике, U = 20 В - конечное значение напряжения на концах проводника, t - текущее время, T = 0.5 с - продолжительность протекания тока, R = 5 Ом - сопротивление проводника, Q - искомое значение заряда. За элементарное время dt через проводник проходит элементарный заряд dq = i*dt (1); при этом по закону Ома: i = u/R (2), откуда dq = (u/R)*dt (3). При этом, по условию, u возрастает во времени равномерно, т.е. меняется по закону u = k*t (4), где k - постоянный коэффициент. Тогда (3) приобретает вид: dq = (k/R)*t*dt (5). Проинтегрировав (5) от 0 до T, получаем: Q = (k/R)*T2/2 (6). Значение k получаем из условия: k*T = U, откуда k = U/T (7), и, подставляя в (6), окончательно: Q = (U/R)*T/2 = (20/5)*0.5/2 = 1 Кл.
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