Math Problem Statement

In persian

در شکل زیر، مقاومت معادل بین دو نقطه A و B چند اهم است؟

Solution

The image you uploaded contains a question related to an electrical circuit. It asks for the equivalent resistance between two points, A and B, in the given circuit.

To solve this, I'll analyze the configuration of resistors and apply the rules for series and parallel combinations.

Let me calculate the equivalent resistance for you.To solve for the equivalent resistance between points A and B in the given circuit, let's analyze the components and their connections:

  1. From the diagram:
    • There are resistors in series and parallel.
    • Some resistors are connected in parallel, and others are in series with them.

Step-by-step solution:

  1. The two resistors (6Ω and 6Ω) are connected in parallel. For resistors in parallel, the equivalent resistance ReqR_{eq} is given by the formula:

    1Req=1R1+1R2\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}

    Substituting the values:

    1Req=16+16=26    Req=3Ω\frac{1}{R_{eq}} = \frac{1}{6} + \frac{1}{6} = \frac{2}{6} \implies R_{eq} = 3 \, \Omega

  2. Now, this 3Ω equivalent resistance is in series with the 3Ω resistor, so we add them:

    Rtotal=3+3=6ΩR_{total} = 3 + 3 = 6 \, \Omega

  3. The next step is to handle the resistors in parallel. The 6Ω equivalent resistance (from the above step) is in parallel with the 1Ω resistor. Using the parallel formula again:

    1Rfinal=16+11=16+1=76    Rfinal=67Ω\frac{1}{R_{final}} = \frac{1}{6} + \frac{1}{1} = \frac{1}{6} + 1 = \frac{7}{6} \implies R_{final} = \frac{6}{7} \, \Omega

Thus, the total equivalent resistance between points A and B is approximately .

Would you like more details or further clarifications on this calculation?

Here are some additional questions related to this topic:

  1. How do you calculate the total resistance of a circuit with only series resistors?
  2. How can you solve circuits with both series and parallel resistors?
  3. What happens to the equivalent resistance in a parallel circuit when more resistors are added?
  4. How does the current distribution change when resistors are in series vs. parallel?
  5. What are the effects of having high and low resistance in parallel circuits?

Tip: When solving complex circuits, always simplify step-by-step, starting with parallel or series combinations, to avoid confusion.

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Math Problem Analysis

Mathematical Concepts

Electric Circuits
Series and Parallel Resistance
Equivalent Resistance

Formulas

Parallel Resistance Formula: 1/R_eq = 1/R1 + 1/R2 + ...
Series Resistance Formula: R_eq = R1 + R2 + ...

Theorems

Ohm's Law

Suitable Grade Level

Grades 10-12