Question

Имеется батарея из четырех аккумуляторов с э. д. с. по 1,2 в и внутренним сопротивлением по 0,2 ом . Батарея замкнута на сопротивление 4 ом. Определить ток батареи в случае, если аккумуляторы соединены: а) последовательно, б) параллельно.

Answer 1

Ответ:

Объяснение:

Дано:

n = 4

ЭДС = 1,2 В

r = 0,2 Ом

R = 4 Ом

___________

I₁ - ?

I₂ - ?

1)

Последовательное соединение.

ЭДС₁ = n·ЭДС = 4·1,2 = 4,8 В

r₁ = n·r = 4·0,2 = 0,8 Ом

I₁ = ЭДС₁ / (R + r₁) = 4,8 / (4 + 0,8) = 1 А

2)

Параллельное соединение.

ЭДС₂ = ЭДС = 1,2 В

r₂ = r/n = 0,2/4 = 0,05 Ом

I₂ = ЭДС₂ / (R + r₂) = 1,2 / (4 + 0,05) ≈ 0,3 А

Answer 2

Calculation of Battery Current in Series Connection

When the batteries are connected in series, the total voltage of the battery pack is the sum of the individual battery voltages. The internal resistances of the batteries also add up. To calculate the current in the battery pack, we can use Ohm's Law, which states that the current (I) is equal to the voltage (V) divided by the total resistance (R).

In this case, we have four batteries with a voltage of 1.2V each and an internal resistance of 0.2 ohms. The battery pack is connected to a load with a resistance of 4 ohms.

To calculate the current in the battery pack when the batteries are connected in series, we need to find the total voltage and the total resistance.

The total voltage (V_total) is the sum of the individual battery voltages: V_total = 1.2V + 1.2V + 1.2V + 1.2V = 4.8V

The total resistance (R_total) is the sum of the internal resistances and the load resistance: R_total = 0.2 ohms + 0.2 ohms + 0.2 ohms + 0.2 ohms + 4 ohms = 4.8 ohms

Now, we can use Ohm's Law to calculate the current (I): I = V_total / R_total = 4.8V / 4.8 ohms = 1A

Therefore, the current in the battery pack when the batteries are connected in series is 1A.

Calculation of Battery Current in Parallel Connection

When the batteries are connected in parallel, the voltage across each battery remains the same, but the total current is divided among the batteries. The internal resistances of the batteries also divide the total resistance.

To calculate the current in the battery pack when the batteries are connected in parallel, we need to find the total voltage and the total resistance.

The total voltage (V_total) remains the same as the voltage of each individual battery: V_total = 1.2V

The total resistance (R_total) is the sum of the inverse of the internal resistances and the inverse of the load resistance: 1/R_total = 1/0.2 ohms + 1/0.2 ohms + 1/0.2 ohms + 1/0.2 ohms + 1/4 ohms 1/R_total = 5/0.2 ohms + 1/4 ohms = 25/1 ohms + 1/4 ohms = 29/4 ohms R_total = 4/29 ohms

Now, we can use Ohm's Law to calculate the current (I): I = V_total / R_total = 1.2V / (4/29 ohms) = 1.2V * (29/4 ohms) = 8.7A

Therefore, the current in the battery pack when the batteries are connected in parallel is 8.7A.

Please let me know if you need any further clarification or assistance.