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.