Electrical circuit with resistors in series and parallel configurations.

To solve the problem of finding the equivalent resistance between points a and d in the given circuit, we need to simplify the circuit step by step. Let's break it down systematically.

Step 1: Identify the Circuit Components

The circuit consists of several resistors connected in series and parallel configurations. The resistors are labeled as \( R_1, R_2, R_3, R_4, R_5, R_6, \) and \( R_7 \).

Step 2: Simplify the Inner Parallel Resistors

First, let's focus on the inner part of the circuit, specifically the resistors \( R_2, R_3, R_4, R_5, R_6, \) and \( R_7 \).

#### Step 2.1: Simplify \( R_6 \) and \( R_7 \)
The resistors \( R_6 \) and \( R_7 \) are in parallel. The equivalent resistance \( R_{67} \) is given by:
\[
R_{67} = \frac{R_6 \cdot R_7}{R_6 + R_7}
\]

#### Step 2.2: Combine \( R_4 \) with \( R_{67} \)
The resistor \( R_4 \) is in series with the parallel combination \( R_{67} \). The equivalent resistance \( R_{467} \) is:
\[
R_{467} = R_4 + R_{67}
\]

#### Step 2.3: Simplify \( R_2 \) and \( R_3 \)
The resistors \( R_2 \) and \( R_3 \) are in series. The equivalent resistance \( R_{23} \) is:
\[
R_{23} = R_2 + R_3
\]

#### Step 2.4: Combine \( R_{23} \) with \( R_{467} \)
The resistors \( R_{23} \) and \( R_{467} \) are in parallel. The equivalent resistance \( R_{23467} \) is:
\[
R_{23467} = \frac{R_{23} \cdot R_{467}}{R_{23} + R_{467}}
\]

#### Step 2.5: Add \( R_5 \)
The resistor \( R_5 \) is in series with the parallel combination \( R_{23467} \). The equivalent resistance \( R_{\text{inner}} \) is:
\[
R_{\text{inner}} = R_5 + R_{23467}
\]

Step 3: Combine with \( R_1 \)

Now, the equivalent resistance \( R_{\text{inner}} \) is in series with \( R_1 \). The total equivalent resistance \( R_{\text{eq}} \) between points a and d is:
\[
R_{\text{eq}} = R_1 + R_{\text{inner}}
\]

Final Expression

Substituting the expressions step by step:
1. \( R_{67} = \frac{R_6 \cdot R_7}{R_6 + R_7} \)
2. \( R_{467} = R_4 + R_{67} \)
3. \( R_{23} = R_2 + R_3 \)
4. \( R_{23467} = \frac{R_{23} \cdot R_{467}}{R_{23} + R_{467}} \)
5. \( R_{\text{inner}} = R_5 + R_{23467} \)
6. \( R_{\text{eq}} = R_1 + R_{\text{inner}} \)

Final Answer

The equivalent resistance between points a and d is:
\[
\boxed{R_1 + R_5 + \frac{(R_2 + R_3)(R_4 + \frac{R_6 R_7}{R_6 + R_7})}{(R_2 + R_3) + (R_4 + \frac{R_6 R_7}{R_6 + R_7})}}
\]