Question

ЭДС батареи E = 24 В. Батарея подключена к сопротивлению R = 16 Ом. Параллельно сопротивлению включен вольтметр с внутренним сопротивлением RV = 1000 Ом. Найдите внутреннее сопротивление батареи Rвн , если показания вольтметра UV = 21,3 В. Рассчитайте показание идеального вольтметра U. Результат дайте в системе СИ и округлите до двух значащих цифр после запятой. Размерность не ставьте!Сопротивление R вн 2 Ом Напряжение ид. вольт. U ??? В

Answer 1

Общее сопротивление нагрузки:
1/R = 1/16 + 1/1000 = 127 /2000
R = 2000/127 = 15,75 Ом
Ток в цепи I = U/R = 21.3/15.75 = 1.35 A
Уравнение всей цепи I = EDS/(R1+R), где R1 - внутреннее сопротивление батареи
1,35 = 24 / (R1+15,75)
24 = 1,35R1+15,75*1,35
1,35R1 = 24 - 21.3      
1,35R1 = 2.7
R1 = 2 Ом

Answer 2

Calculation of Internal Resistance of the Battery (Rвн)

To calculate the internal resistance of the battery (Rвн), we can use the formula:

Rвн = (E - UV) / (UV / RV)

Where: - E is the electromotive force (EДС) of the battery, which is given as 24 V. - UV is the voltage reading on the voltmeter, which is given as 21.3 V. - RV is the internal resistance of the voltmeter, which is given as 1000 Ω.

Substituting the given values into the formula, we get:

Rвн = (24 - 21.3) / (21.3 / 1000)

Calculating this expression, we find:

Rвн ≈ 126.17 Ω

Therefore, the internal resistance of the battery (Rвн) is approximately 126.17 Ω.

Calculation of Ideal Voltmeter Reading (U)

To calculate the ideal voltmeter reading (U), we can use the formula:

U = E - (Rвн * I)

Where: - E is the electromotive force (EДС) of the battery, which is given as 24 V. - Rвн is the internal resistance of the battery, which we calculated as approximately 126.17 Ω. - I is the current flowing through the circuit.

To calculate the current (I), we can use Ohm's Law:

I = UV / (R + RV)

Where: - UV is the voltage reading on the voltmeter, which is given as 21.3 V. - R is the resistance connected in parallel to the voltmeter, which is given as 16 Ω. - RV is the internal resistance of the voltmeter, which is given as 1000 Ω.

Substituting the given values into the formula, we get:

I = 21.3 / (16 + 1000)

Calculating this expression, we find:

I ≈ 0.021 A

Now, substituting the values of E, Rвн, and I into the formula for U, we get:

U = 24 - (126.17 * 0.021)

Calculating this expression, we find:

U ≈ 21.72 V

Therefore, the ideal voltmeter reading (U) is approximately 21.72 V.

Please note that the calculations are based on the given values and assumptions.