Question

Сопротивления резисторов равны R1 = 2 Ом R2 = 1 Ом R3 = 3 Ом R4 = 1 Ом. Определите общее сопротивление участка при последовательном и параллельном соединении резисторов. Начертите схемы электрических цепей

Answer 1

R1 = 2 Ом R2 = 1 Ом R3 = 3 Ом R4 = 1 Ом.

При последовательном соединении сопротивления каждого резистора складываются.

При параллельном соединении общее сопротивление резисторов вычисляется по формуле: R=1/(1/R1+1/R2+1/R3);

a) R=R1+R2+R3; R=1+1+1=3 Ома

б) R=1/(1/1+1/1+1/1)=1/3 Ома

в) R=R1 + 1/(1/1+1/1)=3/2 Ома

г) R=1/(1/1+1/(1+1))=2/3 Ома

Answer 2

Calculating Total Resistance

To calculate the total resistance of the given resistors in both series and parallel connections, we can use the following formulas:

For series connection: The total resistance (R_total) in a series connection is the sum of the individual resistances.

For parallel connection: The total resistance (R_total) in a parallel connection can be calculated using the formula: 1/R_total = 1/R1 + 1/R2 + 1/R3 + ...

Let's calculate the total resistance for both cases.

Series Connection

In a series connection, the total resistance (R_total) is the sum of the individual resistances: R_total = R1 + R2 + R3 + R4

Substituting the given resistance values: R1 = 2 Ω, R2 = 1 Ω, R3 = 3 Ω, R4 = 1 Ω

Total resistance in series connection: R_total = 2 Ω + 1 Ω + 3 Ω + 1 Ω = 7 Ω

Parallel Connection

In a parallel connection, the reciprocal of the total resistance (1/R_total) is the sum of the reciprocals of the individual resistances: 1/R_total = 1/R1 + 1/R2 + 1/R3 + 1/R4

Substituting the given resistance values: R1 = 2 Ω, R2 = 1 Ω, R3 = 3 Ω, R4 = 1 Ω

Total resistance in parallel connection: 1/R_total = 1/2 Ω + 1/1 Ω + 1/3 Ω + 1/1 Ω 1/R_total = 0.5 + 1 + 0.333 + 1 1/R_total = 2.833

Taking the reciprocal of 1/R_total: R_total = 1 / 2.833 R_total ≈ 0.353 Ω

Circuit Diagrams

Here are the circuit diagrams for the series and parallel connections:

Series Connection: ``` --- R1 --- R2 --- R3 --- R4 --- ```

Parallel Connection: ``` ---| R1 |--- | R2 | | R3 | | R4 | ```

These diagrams represent the arrangement of resistors in the respective connections.

I hope this helps! If you have further questions or need additional assistance, feel free to ask.