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Консультация № 131412
09.04.2008, 20:42
0.00 руб.
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К зажимам батареи аккумулятора присоединен нагреватель. ЭДС батареи Е=24 В, внутренее сопротивление r=1 Ом. Нагреватель, включенный в цепь, потребляет мощность 80 Вт. Вычислить силу тока в цепи и КПД источника.
Приложение:
Ответ: 20 А; 0,17; 4 А; 0,83.
Приложение:
Ответ: 20 А; 0,17; 4 А; 0,83.
Обсуждение
12.04.2008, 05:43
общий
это ответ
Здравствуйте, Луковский Серргей Анатольевич!
Мощность P<sub>и</sub>, потребляемая от источника, равна: P<sub>и</sub> = P<sub>н</sub> + ΔP (1), где P<sub>н</sub> - мощность, потребляемая нагревателем, ΔP - потери во внутреннем сопротивлении r. ΔP = I<sup>2</sup>*r (2), где I - сила тока. P<sub>и</sub> = Е*I (3). Из (1), (2) и (3) получаем: Е*I = P<sub>н</sub> + I<sup>2</sup>*r (4), а разделив (4) на r и перенеся всё в левую часть, получаем квадратное уравнение: I<sup>2</sup> - (Е/r)*I + P<sub>н</sub>/r (5). Решив (5): I = Е/(2*r) ± √((Е/(2*r))<sup>2</sup> - P<sub>н</sub>/r), получаем два положительных корня: I = 24/(2*1) ± √((24/(2*1))<sup>2</sup> - 80/1); I<sub>1</sub> = 12 - √(64) = 4 А; I<sub>1</sub> = 12 + √(64) = 20 А. Соответственно внешнее напряжение батареи: U = Е - I*r; U<sub>1</sub> = 24 - 4*1 = 20 В, и КПД источника = 20/24 = 0.833; U<sub>2</sub> = 24 - 20*1 = 4 В, и КПД источника = 4/24 = 0.167.
Мощность P<sub>и</sub>, потребляемая от источника, равна: P<sub>и</sub> = P<sub>н</sub> + ΔP (1), где P<sub>н</sub> - мощность, потребляемая нагревателем, ΔP - потери во внутреннем сопротивлении r. ΔP = I<sup>2</sup>*r (2), где I - сила тока. P<sub>и</sub> = Е*I (3). Из (1), (2) и (3) получаем: Е*I = P<sub>н</sub> + I<sup>2</sup>*r (4), а разделив (4) на r и перенеся всё в левую часть, получаем квадратное уравнение: I<sup>2</sup> - (Е/r)*I + P<sub>н</sub>/r (5). Решив (5): I = Е/(2*r) ± √((Е/(2*r))<sup>2</sup> - P<sub>н</sub>/r), получаем два положительных корня: I = 24/(2*1) ± √((24/(2*1))<sup>2</sup> - 80/1); I<sub>1</sub> = 12 - √(64) = 4 А; I<sub>1</sub> = 12 + √(64) = 20 А. Соответственно внешнее напряжение батареи: U = Е - I*r; U<sub>1</sub> = 24 - 4*1 = 20 В, и КПД источника = 20/24 = 0.833; U<sub>2</sub> = 24 - 20*1 = 4 В, и КПД источника = 4/24 = 0.167.
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