To determine the temperature $$t$$ in the Kelvin scale, we need to use the relationship between the resistance of a wire and temperature. The general formula for the resistance $R$ of a wire as a function of temperature is:

$$ R_t = R_0 (1 + \alpha t) $$

where:

• $$R_t$$ is the resistance at temperature $$t$$
• $$R_0$$ is the resistance at the reference temperature (usually $$0^{\circ} \mathrm{C}$$)
• $$\alpha$$ is the temperature coefficient of resistance
• $$t$$ is the temperature

We are given the following resistances:

• Resistance at $$0^{\circ} \mathrm{C}$$: $$R_0 = 10 \Omega$$
• Resistance at $$100^{\circ} \mathrm{C}$$: $$R_{100} = 10.2 \Omega$$
• Resistance at $$t^{\circ} \mathrm{C}$$: $$R_t = 10.95 \Omega$$

First, we need to find the temperature coefficient of resistance $$\alpha$$. Using the resistance at $$100^{\circ} \mathrm{C}$$:

$$ 10.2 = 10 (1 + \alpha \cdot 100) $$

Solving for $$\alpha$$:

$$ \frac{10.2}{10} = 1 + 100\alpha \implies 1.02 = 1 + 100\alpha \implies 100\alpha = 0.02 \implies \alpha = \frac{0.02}{100} = 0.0002 $$

Now, we can find the temperature $$t$$ using the resistance at $$t^{\circ} \mathrm{C}$$:

$$ 10.95 = 10 (1 + 0.0002 \cdot t) $$

Solving for $$t$$:

$$ \frac{10.95}{10} = 1 + 0.0002 t \implies 1.095 = 1 + 0.0002 t \implies 0.0002 t = 0.095 \implies t = \frac{0.095}{0.0002} = 475 $$

The temperature $$t$$ in Celsius is $$475^{\circ} \mathrm{C}$$. To convert this to the Kelvin scale:

$$ T_{K} = t_{C} + 273.15 = 475 + 273.15 = 748.15 \, \mathrm{K} $$

So, the temperature $$t$$ in Kelvin scale is approximately $$748.15 \, \mathrm{K}$$.