**Effect of Conductivity in Series Combination of Wires**

When two wires of identical dimensions are connected in series, the overall conductivity of the combination is influenced by the conductivities of the metals used in the wires. To understand the effect of conductivity in this combination, let's analyze it in detail.

**1. Understanding Series Combination:**
In a series combination, the wires are connected end-to-end, creating a single path for the flow of electric current. The current passing through each wire is the same, as there is no alternative path for the current to bypass any wire.

**2. Conductivity and Resistance:**
Conductivity (σ) is the measure of a material's ability to conduct electric current. It is the reciprocal of electrical resistivity (ρ), which quantifies a material's opposition to current flow. The higher the conductivity, the lower the resistance.

**3. Resistance in Series Combination:**
In a series combination, the total resistance (R_total) is the sum of the individual resistances (R1 and R2) of the wires. Mathematically, it can be expressed as:
R_total = R1 + R2

**4. Relationship between Conductivity and Resistance:**
The resistance of a wire is inversely proportional to its conductivity. The relationship can be expressed as:
R = ρ * (L/A)
where R is the resistance, ρ is the resistivity, L is the length of the wire, and A is the cross-sectional area of the wire.

**5. Effect of Conductivity in Series Combination:**
Since resistance is inversely proportional to conductivity, the conductivity of the wires affects the overall resistance of the series combination. Let's consider two cases:

- **Case 1: High Conductivity (x > y):** If the first wire (wire 1) has higher conductivity (x) compared to the second wire (wire 2) with lower conductivity (y), the resistance of wire 1 will be lower than wire 2. Consequently, wire 1 will carry a larger proportion of the total current, while wire 2 will carry a smaller proportion. This results in an overall decrease in the resistance of the series combination.

- **Case 2: Low Conductivity (x < y):**="" if="" the="" first="" wire="" (wire="" 1)="" has="" lower="" conductivity="" (x)="" compared="" to="" the="" second="" wire="" (wire="" 2)="" with="" higher="" conductivity="" (y),="" the="" resistance="" of="" wire="" 1="" will="" be="" higher="" than="" wire="" 2.="" as="" a="" result,="" wire="" 1="" will="" carry="" a="" smaller="" proportion="" of="" the="" total="" current,="" while="" wire="" 2="" will="" carry="" a="" larger="" proportion.="" this="" leads="" to="" an="" overall="" increase="" in="" the="" resistance="" of="" the="" series="" />

**In conclusion,** the conductivity of the wires in a series combination directly affects the overall resistance. Higher conductivity in one wire reduces the resistance, while lower conductivity increases the resistance.

X+Y/2