Question

Амперметр может измерять ток не более 2 А. Сопротивление амперметра 0,1 Ом. Каково должно быть сопротивление шунта, присоединённого к амперметру, чтобы можно было измерять ток до 10 A? РЕШИТЬ ЗАДАЧУ 3 СПОСОБАМИ

Answer 1

Ответ:

Объяснение:

Дано:

Iа = 2 A - ток, проходящий  через амперметр

Rа = 0,1 Ом - сопротивление амперметра

I = 10 А - измеряемый ток

_______________

Rш - ?

1 решение

Коэффициент шунтирования:

n = I / Iа = 10 / 2 = 5

Сопротивление шунта:

Rш = Rа / (n - 1)         (1)

Rш = 0,1 / (5 - 1) = 0,025 Ом

2 решение

Поскольку  шунт подключается к амперметру всегда параллельно, то в двух параллельных ветвях токи разветвляются:

Ia / Iш = Rш / Iа

Отсюда:

Rш = Ia·Ra / Iш

Но:

Iш = I - Ia = 10 - 2 = 10 - 2 = 8 A

Тогда:

Rш = Ia·Ra / Iш = 2·0,1 / 8 = 0,025 А

З способ.

Мы показали, что при разных формулах мы получили один и тот же ответ, то сделаем заключение:

При любой правильной формуле ответ будет одним и тем же:

Rш = 0,025 А

Answer 2

Calculation of Shunt Resistance for Ammeter

To determine the resistance of the shunt that needs to be connected to the ammeter in order to measure currents up to 10 A, we can use Ohm's Law. Ohm's Law states that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance.

The ammeter has a maximum current rating of 2 A and a resistance of 0.1 Ω. Let's assume the shunt resistance is represented by Rs.

According to Ohm's Law, the total current passing through the ammeter and the shunt can be calculated as:

Total Current (It) = Current through Ammeter (Ia) + Current through Shunt (Is)

Since the ammeter is connected in series with the shunt, the current passing through both of them is the same. Therefore, we can write:

It = Ia = Is

Given that the maximum current rating of the ammeter is 2 A, we have:

It = Ia = Is = 2 A

To measure currents up to 10 A, the shunt should carry the remaining current. Therefore, the current passing through the shunt can be calculated as:

Is = It - Ia = 10 A - 2 A = 8 A

Now, we can use Ohm's Law to calculate the resistance of the shunt:

Is = Vs / Rs

Where: - Is is the current passing through the shunt (8 A) - Vs is the voltage across the shunt (which is equal to the voltage across the ammeter since they are connected in series) - Rs is the resistance of the shunt (to be determined)

Rearranging the equation, we get:

Rs = Vs / Is

Since the voltage across the ammeter is negligible compared to the voltage across the shunt, we can assume that the voltage across the shunt is equal to the total voltage applied. Therefore, we can write:

Rs = Vt / Is

Given that the voltage across the shunt is equal to the total voltage applied, we can calculate the voltage using Ohm's Law:

Vt = It * (Ra + Rs)

Where: - Vt is the total voltage applied - It is the total current passing through the ammeter and the shunt (10 A) - Ra is the resistance of the ammeter (0.1 Ω) - Rs is the resistance of the shunt (to be determined)

Substituting the values, we have:

Vt = 10 A * (0.1 Ω + Rs)

Now, we can substitute the value of Vt into the equation for Rs:

Rs = (10 A * (0.1 Ω + Rs)) / 8 A

Simplifying the equation, we get:

Rs = (1 Ω + 0.1 Rs) / 0.8

Multiplying both sides by 0.8, we have:

0.8 Rs = 1 Ω + 0.1 Rs

Simplifying further, we get:

0.7 Rs = 1 Ω

Finally, solving for Rs, we have:

Rs = 1 Ω / 0.7 ≈ 1.43 Ω

Therefore, the resistance of the shunt that needs to be connected to the ammeter in order to measure currents up to 10 A is approximately 1.43 Ω.

Please note that this calculation assumes ideal conditions and neglects any internal resistance or other factors that may affect the accuracy of the measurement.