Using the laws of combination of resistances, calculate the equivalent resistance between points A and B in the given circuit.

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Points to Remember:

  • Ohm’s Law: V = IR (Voltage = Current x Resistance)
  • Series Combination: Req = R1 + R2 + … + Rn
  • Parallel Combination: 1/Req = 1/R1 + 1/R2 + … + 1/Rn

Introduction:

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This question requires a factual and analytical approach to determine the equivalent resistance between points A and B in a given circuit. It necessitates applying the laws of combination of resistances – specifically, understanding how resistances in series and parallel configurations affect the overall resistance of the circuit. No circuit diagram is provided in the prompt, so I will assume a simple example to demonstrate the process. Let’s assume a circuit with three resistors: R1, R2, and R3. The exact configuration will determine the method of calculation.

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1. Identifying the Circuit Configuration:

To calculate the equivalent resistance, we must first determine how the resistors are connected. Are they connected in series (end-to-end), in parallel (side-by-side), or a combination of both? A diagram is crucial for this step. Without a specific diagram, I will illustrate with two examples:

Example 1: Series Combination

If R1, R2, and R3 are connected in series between points A and B, the equivalent resistance (Req) is simply the sum of the individual resistances:

Req = R1 + R2 + R3

Example 2: Parallel Combination

If R1, R2, and R3 are connected in parallel between points A and B, the equivalent resistance is calculated as follows:

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

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Therefore, Req = 1 / (1/R1 + 1/R2 + 1/R3)

Example 3: Series-Parallel Combination

More complex circuits involve a combination of series and parallel connections. In such cases, we solve the circuit step-by-step. First, we simplify the parallel sections to find their equivalent resistances. Then, we treat these equivalent resistances as if they were in series and calculate the total equivalent resistance.

2. Calculation and Units:

Once the configuration is identified, the appropriate formula is applied. Remember that resistance is measured in Ohms (Ω). The calculated equivalent resistance will also be in Ohms.

Example (Series-Parallel Combination):

Let’s assume R1 = 10Ω, R2 = 20Ω, and R3 = 30Ω. If R1 and R2 are in parallel, and their equivalent is in series with R3, we first calculate the equivalent resistance of the parallel combination:

1/Rparallel = 1/10Ω + 1/20Ω = 3/20Ω
Rparallel = 20Ω/3 ≈ 6.67Ω

Then, we add this equivalent resistance to R3:

Req = Rparallel + R3 = 6.67Ω + 30Ω = 36.67Ω

Conclusion:

Calculating the equivalent resistance in a circuit requires a clear understanding of the circuit’s configuration and the application of the appropriate formulas for series and parallel combinations. The process involves systematically simplifying the circuit, step-by-step, until a single equivalent resistance is obtained. The units of resistance are always Ohms (Ω). Without a specific circuit diagram, a precise calculation cannot be performed. However, the examples provided illustrate the methodology for solving various circuit configurations. A thorough understanding of these principles is essential for analyzing and designing electrical circuits effectively. Further exploration into more complex circuit analysis techniques, such as Kirchhoff’s laws, can enhance understanding for more intricate networks.

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