Question

9.Три резистора 2 Ом, 4 Ом, 6 Ом соединены параллельно, последовательно к ним подключён резистор 8 Ом. Напряжение на батарее 180 В. Найти токи и напряжения в каждом резисторе.

Answer 1

Решение в 2-х прикрепленных файлах

Answer 2

Calculation of Current and Voltage in Each Resistor

To find the currents and voltages in each resistor, we can use Ohm's Law and the rules for parallel and series resistances.

Given information: - Three resistors: 2 Ω, 4 Ω, and 6 Ω, connected in parallel. - A resistor of 8 Ω connected in series with the parallel combination. - Battery voltage: 180 V.

To solve this problem, we'll follow these steps:

1. Calculate the equivalent resistance of the parallel combination of the three resistors. 2. Calculate the total current flowing through the circuit using Ohm's Law. 3. Calculate the voltage drop across the parallel combination of resistors. 4. Calculate the current flowing through each resistor using Ohm's Law. 5. Calculate the voltage drop across each resistor using Ohm's Law.

Let's proceed with the calculations:

Step 1: Calculate the Equivalent Resistance of the Parallel Combination

The formula to calculate the equivalent resistance of resistors connected in parallel is:

1/Req = 1/R1 + 1/R2 + 1/R3

Substituting the given resistor values:

1/Req = 1/2 + 1/4 + 1/6

Calculating the equivalent resistance:

1/Req = 3/6 + 2/6 + 1/6 = 6/6 = 1

Taking the reciprocal of both sides:

Req = 1 Ω

Therefore, the equivalent resistance of the parallel combination is 1 Ω.

Step 2: Calculate the Total Current

Using Ohm's Law (V = IR), we can calculate the total current flowing through the circuit:

V = I * Req

Substituting the given values:

180 V = I * 1 Ω

Solving for I:

I = 180 A

Therefore, the total current flowing through the circuit is 180 A.

Step 3: Calculate the Voltage Drop Across the Parallel Combination

Since the parallel combination of resistors is connected in series with an 8 Ω resistor, the voltage drop across the parallel combination will be the same as the voltage drop across the 8 Ω resistor.

Therefore, the voltage drop across the parallel combination is also 180 V.

Step 4: Calculate the Current Flowing Through Each Resistor

Using Ohm's Law (V = IR), we can calculate the current flowing through each resistor:

For the parallel combination of resistors: 180 V = I_parallel * 1 Ω

Solving for I_parallel: I_parallel = 180 A

Since the resistors are connected in parallel, the current flowing through each resistor will be the same as the current flowing through the parallel combination.

Therefore, the current flowing through each resistor is 180 A.

Step 5: Calculate the Voltage Drop Across Each Resistor

Using Ohm's Law (V = IR), we can calculate the voltage drop across each resistor:

For the 2 Ω resistor: V_2Ω = I * 2 Ω = 180 A * 2 Ω = 360 V

For the 4 Ω resistor: V_4Ω = I * 4 Ω = 180 A * 4 Ω = 720 V

For the 6 Ω resistor: V_6Ω = I * 6 Ω = 180 A * 6 Ω = 1080 V

Therefore, the voltage drop across the 2 Ω resistor is 360 V, the voltage drop across the 4 Ω resistor is 720 V, and the voltage drop across the 6 Ω resistor is 1080 V.

To summarize:

- The current flowing through each resistor is 180 A. - The voltage drop across the 2 Ω resistor is 360 V. - The voltage drop across the 4 Ω resistor is 720 V. - The voltage drop across the 6 Ω resistor is 1080 V.

Please note that the calculated values assume ideal conditions and do not take into account any internal resistance of the battery or other factors that may affect the circuit.