Question

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

• A. 1694\( ^\circ \)C
• B. 1235\( ^\circ \)C
• C. 694\( ^\circ \)C
• D. 1667\( ^\circ \)C

Answer 1

The Correct Option is A

To determine the temperature of the toaster when connected to a 220 V supply with a current of 2.75 A, the following parameters are provided:

• Initial resistance at room temperature (\(27^\circ \text{C}\)): \( R_0 = 60 \, \Omega \)
• Voltage supply: \( V = 220 \, \text{V} \)
• Current: \( I = 2.75 \, \text{A} \)
• Temperature coefficient of resistance: \( \alpha = 2 \times 10^{-4} / ^\circ \text{C} \)

The toaster's final resistance at operating temperature is calculated using Ohm's Law:

\(R = \frac{V}{I}\)

Substituting the given values yields:

\(R = \frac{220}{2.75} = 80 \, \Omega\)

Let \( T \) represent the final temperature. The relationship between resistance and temperature is expressed as:

\(R = R_0(1 + \alpha(T - T_0))\)

Plugging in the known values:

\(80 = 60 \times (1 + 2 \times 10^{-4} \times (T - 27))\)

Solving for \( T \):

\(1.3333 = 1 + 2 \times 10^{-4} \times (T - 27)\)
\(0.3333 = 2 \times 10^{-4} \times (T - 27)\)
\(T - 27 = \frac{0.3333}{2 \times 10^{-4}}\)
\(T - 27 = 1666.5\)
\(T = 1666.5 + 27 = 1693.5\)

Therefore, the toaster reaches a temperature of approximately \( 1694^\circ \text{C} \).

The correct answer is: 1694\( ^\circ \)C