Question

2 проводника сопротивлением по 20 Ом соединены параллельно. Последовательно к ним подключен проводник сопротивлением 5 Ом. Общее напряжение 30 В. Найти токи на каждом проводнике.

Answer 1

1) При параллельном соединении проводников с одинаковым сопротивлением по R каждое

Rобщ=R/n, где n - число ветвей.

У нас параллельное соединение

R1,2=20/2=10 Ом

ИЛИ 1/R1,2=1/R1 + 1/R2=1/20 + 1/20=2/20=1/10, R1,2=10/1=10 Ом.

2) Теперь последовательно 10 и 5 Ом

Rобщ=10+5=15 Ом

3) I=U/Rобщ=30/15=2 А; это сила тока в неразветвленной части цепи через проводник в 5 Ом.  

4) т.к. сопротивления равные, то по ним ток идет одинаковый по 1 А, разветвляется поровну.

Ответ: I1=I2=1 A;  I=2 A.  

Answer 2

Calculation of Currents in the Circuit

To find the currents in each conductor, we can use Ohm's Law, which states that the current flowing through a conductor is equal to the voltage across it divided by its resistance.

Given: - Two conductors with resistances of 20 Ω each, connected in parallel. - Another conductor with a resistance of 5 Ω connected in series with the parallel combination. - The total voltage across the circuit is 30 V.

To find the currents in each conductor, we can follow these steps:

1. Calculate the equivalent resistance of the parallel combination of the two 20 Ω resistors. 2. Calculate the total resistance of the circuit by adding the resistance of the series-connected 5 Ω resistor to the equivalent resistance of the parallel combination. 3. Use Ohm's Law to calculate the current flowing through the circuit. 4. Calculate the current flowing through each conductor using the current divider rule.

Let's perform the calculations step by step.

Step 1: Calculate the Equivalent Resistance of the Parallel Combination

When two resistors are connected in parallel, the equivalent resistance can be calculated using the formula:

1/Req = 1/R1 + 1/R2

In this case, R1 = R2 = 20 Ω. Substituting the values into the formula:

1/Req = 1/20 + 1/20

Simplifying the equation:

1/Req = 2/20

1/Req = 1/10

Taking the reciprocal of both sides:

Req = 10 Ω

Therefore, the equivalent resistance of the parallel combination is 10 Ω.

Step 2: Calculate the Total Resistance of the Circuit

To find the total resistance of the circuit, we need to add the resistance of the series-connected 5 Ω resistor to the equivalent resistance of the parallel combination.

Total Resistance (Rtotal) = Req + 5

Substituting the values:

Rtotal = 10 + 5

Rtotal = 15 Ω

Therefore, the total resistance of the circuit is 15 Ω.

Step 3: Calculate the Current Flowing through the Circuit

Using Ohm's Law, we can calculate the current flowing through the circuit:

Current (I) = Voltage (V) / Total Resistance (Rtotal)

Substituting the values:

I = 30 / 15

I = 2 A

Therefore, the current flowing through the circuit is 2 A.

Step 4: Calculate the Currents in Each Conductor

To calculate the currents in each conductor, we can use the current divider rule. According to the current divider rule, the current flowing through each branch of a parallel circuit is inversely proportional to the resistance of that branch.

Let's denote the currents in the two 20 Ω resistors as I1 and I2, and the current in the 5 Ω resistor as I3.

Using the current divider rule:

I1 = (R2 / (R1 + R2)) * I

I2 = (R1 / (R1 + R2)) * I

I3 = I

Substituting the values:

I1 = (20 / (20 + 20)) * 2

I1 = (20 / 40) * 2

I1 = 0.5 A

I2 = (20 / (20 + 20)) * 2

I2 = (20 / 40) * 2

I2 = 0.5 A

I3 = 2 A

Therefore, the currents in each conductor are as follows: - The current in each of the two 20 Ω resistors is 0.5 A. - The current in the 5 Ω resistor is 2 A.

Please note that the calculations provided above are based on the given information and assumptions.