An electric toaster has resistance of $$60 \text{ } \Omega$$ at room temperature $$(27°C)$$. The toaster is connected to a $$220 \text{ V}$$ supply. If the current flowing through it reaches $$2.75 \text{ A}$$, the temperature attained by toaster is around: (if $$\alpha = 2 \times 10^{-4} \text{ °C}^{-1}$$)

The resistance of a conductor varies with temperature according to:

$$R = R_0(1 + \alpha \Delta T)$$

where $$R_0$$ is the resistance at the reference temperature, $$\alpha$$ is the temperature coefficient of resistance, and $$\Delta T$$ is the change in temperature.

Given: $$R_0 = 60 \text{ } \Omega$$ at $$27°C$$, supply voltage $$= 220 \text{ V}$$, current $$= 2.75 \text{ A}$$, $$\alpha = 2 \times 10^{-4} \text{ °C}^{-1}$$.

First, find the resistance at the operating temperature:

$$R = \frac{V}{I} = \frac{220}{2.75} = 80 \text{ } \Omega$$

Now apply the temperature-resistance relation:

$$80 = 60(1 + 2 \times 10^{-4} \times \Delta T)$$

$$\frac{80}{60} = 1 + 2 \times 10^{-4} \times \Delta T$$

$$\frac{4}{3} = 1 + 2 \times 10^{-4} \times \Delta T$$

$$\frac{1}{3} = 2 \times 10^{-4} \times \Delta T$$

$$\Delta T = \frac{1}{3 \times 2 \times 10^{-4}} = \frac{10^4}{6} \approx 1667°C$$

The final temperature is:

$$T = 27 + 1667 = 1694°C$$

The correct answer is $$1694°C$$.