An electric toaster has resistance of 60 Ω at room temperature (27° C). The toaster is connected to a 220 V supply. If the current flowing through it reaches 2.75 A, the temperature attained by toaster is around : ( if α=2 × 10⁻⁴/° C)

Solution

Physics sir · 4 steps

Get the hot resistance from V/I first, then let R = R₀(1 + α Δ T) give the temperature rise.

1. Hot resistance. Once the toaster heats up, Ohm's law gives its resistance: R = V/I = 220/2.75 = 80 Ω. It has risen from 60 Ω because the element is hotter.

   R = R₀(1 + α Δ T)

2. Find the rise. 80 = 60(1 + 2 × 10⁻⁴ Δ T), so 2 × 10⁻⁴ Δ T = 80/60 - 1 = 1/3. That gives Δ T = 1/(3 × 2 × 10⁻⁴) ≈ 1667 °C.
3. Add room temperature. Δ T is only the rise above 27 °C. The final temperature is 27 + 1667 = 1694 °C.
4. So. The toaster reaches about 1694 °C, which is option (d).

The idea to keep. The formula R = R₀(1 + α Δ T) gives a temperature change, not a temperature. Always add the starting temperature back before you pick an option.

Answer from the NTA final answer key. Solution by PrepWiser.