Question

!!!1СРОЧНО ПОЖАЛУЙСТА!!! Два провідники опорами 10 і 15 Ом увімкнено до мережі, напруга в якій дорівнює 100 В. Визначте потужність електричного струму в кожному провіднику, якщо провідники з’єднати: а) послідовно; б) паралельно

Answer 1

Ответ:

а) При з'єднанні провідників послідовно, загальний опір мережі буде:

R = R1 + R2 = 10 Ом + 15 Ом = 25 Ом

Сила струму в мережі буде:

I = V/R = 100 В / 25 Ом = 4 А

Закон Ома дозволяє обчислити потужність в кожному провіднику:

P1 = I^2R1 = 4^210 Ом = 160 Вт

P2 = I^2R2 = 4^215 Ом = 240 Вт

Отже, потужність в першому провіднику становить 160 Вт, а в другому - 240 Вт.

б) При з'єднанні провідників паралельно, загальний опір мережі буде:

1/R = 1/R1 + 1/R2 = 1/10 Ом + 1/15 Ом = 1/6 Ом

R = 6 Ом

Сила струму в мережі буде:

I = V/R = 100 В / 6 Ом ≈ 16,67 А

Потужність в кожному провіднику обчислюється за формулою:

P = I^2*R

P1 = 16,67^210 Ом ≈ 2781 Вт

P2 = 16,67^215 Ом ≈ 4171 Вт

Отже, потужність в першому провіднику становить близько 2781 Вт, а в другому - близько 4171 Вт.

Объяснение:Ось

Answer 2

Calculation of Power in Series and Parallel Circuits

To determine the power in each conductor when connected in series and parallel, we need to use Ohm's Law and the formulas for power.

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. Mathematically, it can be expressed as:

V = I * R

Where: - V is the voltage across the conductor, - I is the current flowing through the conductor, and - R is the resistance of the conductor.

The formula for power is given by:

P = V * I

Where: - P is the power, - V is the voltage across the conductor, and - I is the current flowing through the conductor.

Let's calculate the power in each conductor when connected in series and parallel.

a) Series Connection

In a series connection, the total resistance is the sum of the individual resistances:

R_total = R1 + R2

Given: - R1 = 10 Ω - R2 = 15 Ω - V = 100 V

To find the current flowing through the circuit, we can rearrange Ohm's Law:

I = V / R_total

Substituting the given values:

I = 100 V / (10 Ω + 15 Ω) = 100 V / 25 Ω = 4 A

Now, we can calculate the power in each conductor using the formula:

P = V * I

For the first conductor (R1): P1 = V * I = 100 V * 4 A = 400 W

For the second conductor (R2): P2 = V * I = 100 V * 4 A = 400 W

Therefore, the power in each conductor when connected in series is 400 W.

b) Parallel Connection

In a parallel connection, the voltage across each conductor is the same, and the total current is the sum of the individual currents.

Given: - R1 = 10 Ω - R2 = 15 Ω - V = 100 V

To find the total resistance, we can use the formula:

1 / R_total = 1 / R1 + 1 / R2

Substituting the given values:

1 / R_total = 1 / 10 Ω + 1 / 15 Ω = (3 + 2) / (30 Ω) = 5 / 30 Ω = 1 / 6 Ω

Taking the reciprocal of both sides:

R_total = 6 Ω

To find the total current flowing through the circuit, we can use Ohm's Law:

I_total = V / R_total = 100 V / 6 Ω ≈ 16.67 A

Now, we can calculate the current in each conductor using the formula:

I = V / R

For the first conductor (R1): I1 = V / R1 = 100 V / 10 Ω = 10 A

For the second conductor (R2): I2 = V / R2 = 100 V / 15 Ω ≈ 6.67 A

Finally, we can calculate the power in each conductor using the formula:

P = V * I

For the first conductor (R1): P1 = V * I1 = 100 V * 10 A = 1000 W

For the second conductor (R2): P2 = V * I2 = 100 V * 6.67 A ≈ 667 W

Therefore, the power in each conductor when connected in parallel is approximately 1000 W for the first conductor and 667 W for the second conductor.

To summarize: - When connected in series, the power in each conductor is 400 W. - When connected in parallel, the power in the first conductor is approximately 1000 W, and the power in the second conductor is approximately 667 W.

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