Introduction:
In the given network of 6 wires, each wire has the same electrical conductance (C). We need to determine the effective resistance between points A and B in this network.

Analysis:
To solve this problem, we can use the concept of equivalent resistance. The equivalent resistance is the single resistor that can replace the entire network without changing the original circuit's behavior.

Series and Parallel Combination:
To determine the effective resistance between A and B, we need to analyze the circuit and identify any series and parallel combinations of resistors.

Series Combination:
- When two resistors are connected in series, their resistances add up.
- In the given network, if two wires share the same current, they are in series.

Parallel Combination:
- When two resistors are connected in parallel, their reciprocals (1/R) add up.
- In the given network, if two wires share the same voltage, they are in parallel.

Approach:
1. Identify series and parallel combinations of wires in the network.
2. Calculate the equivalent resistance for each combination.
3. Replace each series combination with its equivalent resistance.
4. Replace each parallel combination with its equivalent resistance.
5. Repeat steps 1-4 until the entire network is reduced to a single equivalent resistance.

Solution:
1. The given network has 6 wires, all with the same conductance (C).

2. Let's analyze the network step by step:
- Wires 1 and 2 are in series, as they share the same current.
- Wires 3 and 4 are also in series.
- Wires 5 and 6 are in series.

3. The equivalent resistance for each series combination is simply the sum of their resistances:
- The equivalent resistance of wires 1 and 2 is 2C.
- The equivalent resistance of wires 3 and 4 is 2C.
- The equivalent resistance of wires 5 and 6 is 2C.

4. We can now replace each series combination with its equivalent resistance:
- Replace wires 1 and 2 with a single wire of resistance 2C.
- Replace wires 3 and 4 with a single wire of resistance 2C.
- Replace wires 5 and 6 with a single wire of resistance 2C.

5. Now, we have three wires remaining in parallel: the equivalent resistance of wires 2C, 2C, and 2C in parallel is given by:
1/Req = 1/2C + 1/2C + 1/2C = 3/2C
Req = 2C/3

6. Therefore, the effective resistance between points A and B in the given network is 2C/3.

Conclusion:
The effective resistance between points A and B in the network of 6 wires, each with the same electrical conductance (C), is 2C/3. This was determined by identifying series and parallel combinations of wires and calculating their equivalent resistances.

The effective resistance between points A and B in the network of 6 wires can be calculated using the concept of electrical conductance and resistance. Let's analyze the network step by step to determine the effective resistance.

1. Identifying the Network:
First, let's identify the network and label the wires and points for better understanding. The network consists of 6 wires and two points, A and B. We will refer to the wires as W1, W2, W3, W4, W5, and W6.

2. Equivalent Resistance of Parallel Wires:
Since all the wires have the same electrical conductance (C), they can be considered parallel to each other. The equivalent conductance of parallel wires is given by the sum of individual conductances. Therefore, the equivalent conductance (Ce) of the network is:

Ce = C + C + C + C + C + C = 6C

3. Calculating the Effective Resistance:
The effective resistance (Re) between points A and B is the reciprocal of the equivalent conductance. Therefore, we can calculate Re using the formula:

Re = 1 / Ce

4. Simplifying the Formula:
To simplify the formula, we can substitute the value of Ce:

Re = 1 / (6C)

5. Final Result:
The effective resistance between points A and B in the network of 6 wires is given by:

Re = 1 / (6C)

This means that the effective resistance is inversely proportional to the electrical conductance of each wire. As the conductance increases, the effective resistance decreases.

In conclusion, the effective resistance between points A and B in the network of 6 wires is given by Re = 1 / (6C), where C represents the electrical conductance of each wire. It is important to note that this analysis assumes an ideal scenario with no additional resistors or complex circuit elements in the network.