https://file.aiquickdraw.com/mathbot/file/1727477839870858rnoqt.jpg

The circuit shown in the image contains resistors in both series and parallel configurations. Here's the step-by-step method to find the equivalent resistance \( R_{\text{eq}} \).

### Step 1: Identify Parallel and Series Combinations

From the diagram:
- \( R_1 = 9 \, \Omega \)
- \( R_2 = 7 \, \Omega \)
- \( R_3 = 9 \, \Omega \)
- \( R_4 = 7 \, \Omega \)

The resistors are arranged such that:
- \( R_2 \) and \( R_4 \) are in series.
- \( R_1 \) is in parallel with the combination of \( R_2 \) and \( R_4 \).
- \( R_3 \) is also in parallel with the combination of \( R_2 \) and \( R_4 \).

### Step 2: Calculate Series Combination of \( R_2 \) and \( R_4 \)
Resistors in series are added directly:
\[
R_{24} = R_2 + R_4 = 7 \, \Omega + 7 \, \Omega = 14 \, \Omega
\]

### Step 3: Calculate Parallel Combination of \( R_1 \), \( R_3 \), and \( R_{24} \)
The formula for resistors in parallel is:
\[
\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_3} + \frac{1}{R_{24}}
\]
Substitute the values:
\[
\frac{1}{R_{\text{eq}}} = \frac{1}{9} + \frac{1}{9} + \frac{1}{14}
\]

### Step 4: Compute the Result

Let's calculate \( R_{\text{eq}} \).The equivalent resistance \( R_{\text{eq}} \) of the given circuit is approximately \( 3.41 \, \Omega \).

Would you like further details or have any other questions?

Here are five related questions to expand your understanding:
1. How does adding resistors in series affect the total resistance?
2. How does adding resistors in parallel affect the total resistance?
3. What would happen if the values of \( R_2 \) and \( R_4 \) were different?
4. How would the equivalent resistance change if the circuit configuration were altered (e.g., if \( R_1 \) and \( R_2 \) were in series)?
5. What are some practical applications of series and parallel resistor combinations in electrical circuits?

**Tip:** In parallel circuits, the equivalent resistance is always less than the smallest resistor value.

In the given circuit, R1 = 9 Ω, R2 = 7 Ω, R3 = 9 Ω, and R4 = 7 Ω. Find Req.

This example demonstrates how to calculate the equivalent resistance in a circuit that includes both series and parallel resistors. Resistors R1, R2, R3, and R4 are given, and the solution uses both series and parallel formulas to find the total resistance. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation