Three resistors, R1 = 2.09 Ω, R2 = 4.77 Ω, and R3 = 6.55 Ω are connected by ideal metal wires, as shown in the figure. What is the resistance of a single resistor that can be used to replace all R1, R2 and R3without changing the function of circuit (in Ω)?

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Three resistors, R1 = 2.09 Ω, R2 = 4.77 Ω, and R3 = 6.55 Ω are connected by ideal metal wires, as shown in the figure. What is the resistance of a single resistor that can be used to replace all R1, R2 and R3without changing the function of circuit (in Ω)?

This image depicts an electrical circuit diagram featuring three resistors. Here's a detailed explanation:

### Resistor Circuit Diagram Explanation

This diagram illustrates a combination of series and parallel resistors within an electrical circuit. The elements are arranged as follows:

- **Resistor R1** is connected in series between points a and b.
- Following Resistor R1, the circuit divides into two branches. Each branch contains one of the two resistors:
  - **Resistor R2** is placed on the upper branch.
  - **Resistor R3** is placed on the lower branch.

### Circuit Components and Configuration

- **Point a**: This is the starting point of the circuit.
- **Resistor R1**: It is directly connected to point a and forms a series connection with the rest of the circuit.
- **Parallel Configuration**: After Resistor R1, the circuit splits into two branches, forming a parallel configuration of:
  - **Resistor R2**: Connected in one branch parallel to Resistor R3.
  - **Resistor R3**: Connected in the other branch parallel to Resistor R2.
- **Point b**: This is the end point where the parallel branches converge back to form a single pathway.

### Implications

- **Total Resistance**: The total resistance between points a and b is the sum of the resistance of R1 and the combined parallel resistance of R2 and R3.
- **Current Distribution**: The current flowing through the circuit will split at the parallel configuration, with parts of the current flowing through Resistor R2 and Resistor R3 according to their resistance values.

This configuration is commonly analyzed in basic electrical engineering and physics courses to understand the principles of series and parallel circuits and their implications on current and voltage distribution.
Transcribed Image Text:This image depicts an electrical circuit diagram featuring three resistors. Here's a detailed explanation: ### Resistor Circuit Diagram Explanation This diagram illustrates a combination of series and parallel resistors within an electrical circuit. The elements are arranged as follows: - **Resistor R1** is connected in series between points a and b. - Following Resistor R1, the circuit divides into two branches. Each branch contains one of the two resistors: - **Resistor R2** is placed on the upper branch. - **Resistor R3** is placed on the lower branch. ### Circuit Components and Configuration - **Point a**: This is the starting point of the circuit. - **Resistor R1**: It is directly connected to point a and forms a series connection with the rest of the circuit. - **Parallel Configuration**: After Resistor R1, the circuit splits into two branches, forming a parallel configuration of: - **Resistor R2**: Connected in one branch parallel to Resistor R3. - **Resistor R3**: Connected in the other branch parallel to Resistor R2. - **Point b**: This is the end point where the parallel branches converge back to form a single pathway. ### Implications - **Total Resistance**: The total resistance between points a and b is the sum of the resistance of R1 and the combined parallel resistance of R2 and R3. - **Current Distribution**: The current flowing through the circuit will split at the parallel configuration, with parts of the current flowing through Resistor R2 and Resistor R3 according to their resistance values. This configuration is commonly analyzed in basic electrical engineering and physics courses to understand the principles of series and parallel circuits and their implications on current and voltage distribution.
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