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Find the equivalent resistance of the given figure

To find the equivalent resistance of a circuit, we need to analyze how the resistors are arranged—whether they are in series, parallel, or a combination of both. Since I can't see the figure you're referring to, I'll guide you through the general process of calculating equivalent resistance, which you can apply to your specific circuit.

Understanding Series and Parallel Resistors

Resistors can be connected in two primary ways:

• Series Connection: In a series circuit, the resistors are connected end-to-end. The total or equivalent resistance (R_eq) is simply the sum of the individual resistances.
• Parallel Connection: In a parallel circuit, the resistors are connected across the same two points. The formula for equivalent resistance in parallel is a bit different and is given by:

1/R_eq = 1/R₁ + 1/R₂ + 1/R₃ + ...

Step-by-Step Calculation

Let’s break down the process into manageable steps:

1. Identify the Configuration: Look at the circuit diagram and determine which resistors are in series and which are in parallel.
2. Calculate Series Resistors: For resistors in series, simply add their resistances together. For example, if R₁ = 2Ω and R₂ = 3Ω, then R_eq = R₁ + R₂ = 2Ω + 3Ω = 5Ω.
3. Calculate Parallel Resistors: For resistors in parallel, use the formula mentioned earlier. If R₁ = 4Ω and R₂ = 4Ω, then:

1/R_eq = 1/4 + 1/4 = 1/2, so R_eq = 2Ω.

Combining Series and Parallel

In many circuits, you will have a combination of series and parallel resistors. In such cases, follow these steps:

• Calculate the equivalent resistance for the series or parallel groups first.
• Redraw the circuit with the equivalent resistances replaced.
• Repeat the process until you have a single equivalent resistance for the entire circuit.

Example Scenario

Imagine a circuit with two resistors in series (R₁ = 3Ω and R₂ = 5Ω) and a third resistor (R₃ = 6Ω) in parallel with the combination of R₁ and R₂. Here’s how you would calculate the equivalent resistance:

1. First, calculate the series resistors: R_series = R₁ + R₂ = 3Ω + 5Ω = 8Ω.
2. Next, calculate the equivalent resistance of R_series in parallel with R₃: 1/R_eq = 1/8 + 1/6.
3. Finding a common denominator (24), we get: 1/R_eq = 3/24 + 4/24 = 7/24, so R_eq = 24/7 ≈ 3.43Ω.

By following these steps, you can find the equivalent resistance for any circuit configuration. If you have a specific circuit diagram, apply these principles to determine the equivalent resistance effectively.