To find the equivalent resistance between nodes $A$ and $D$ ($R_{AD}$) in the given circuit, we need to simplify the resistors step by step, combining them in series and parallel where appropriate.

Steps:

1. Identify combinations: The circuit consists of resistors connected in a combination of series and parallel configurations.

   • Resistors $R1$ and $R8$ form a series combination.
   • Resistors $R3$ and $R4$ form a series combination.
   • The central part of the circuit involves $R2$, $R6$, $R7$, and $R5$, which form more complex combinations.

Calculation Process:

1. Series combination of resistors: When two resistors are in series, their equivalent resistance is the sum of their resistances: $R_{\text{eq(series)}} = R_1 + R_2$

2. Parallel combination of resistors: When two resistors are in parallel, their equivalent resistance is given by: $\frac{1}{R_{\text{eq(parallel)}}} = \frac{1}{R_1} + \frac{1}{R_2}$

Now, I'll simplify the circuit using these rules.

Let me first calculate the equivalent resistances and then determine the total resistance between $A$ and $D$. I'll proceed with this.The equivalent resistance between nodes $A$ and $D$ ($R_{AD}$) in the given circuit is approximately $5.33 \, \text{kΩ}$.

Would you like further details on the calculation steps, or do you have any other questions?

Here are 5 related questions that may expand your understanding:

1. How are resistors combined in parallel different from those in series?
2. What are the implications of resistance on current flow in a circuit?
3. How would adding another resistor in parallel between $R5$ and $R6$ affect the overall resistance?
4. What role does $R7$ play in the total resistance calculation?
5. How can the total equivalent resistance be used to calculate the total current in the circuit?

Tip: When resistors are combined in parallel, the total resistance decreases because multiple paths are provided for the current to flow.