To determine the resistance of a resistor at a higher temperature, we use the formula for the temperature dependence of resistors:
\(R_t = R_0 (1 + \alpha \Delta t)\)
where:
- \(R_t\) is the resistance at temperature \(t\) degrees Celsius,
- \(R_0\) is the resistance at a reference temperature (usually 0 degrees Celsius),
- \(\alpha\) is the temperature coefficient of resistance,
- \(\Delta t\) is the change in temperature.
Given:
- \(R_0 = 10 \text{ Ohms at } 0^\circ \text{C}\)
- \(\alpha = 0.04 \text{ per degree Celsius}\)
- Desired temperature \(t = 40^\circ \text{C}\)
Therefore, the change in temperature \(\Delta t\) is:
\(\Delta t = 40 - 0 = 40^\circ \text{C}\)
Now, substituting in the formula:
\(R_{40} = 10 (1 + 0.04 \times 40)\)
\(R_{40} = 10 (1 + 1.6)\)
\(R_{40} = 10 \times 2.6\)
\(R_{40} = 26 \text{ Ohms}\)
Hence, the resistance of the resistor at 40 degrees Celsius is 26 Ohms.
Therefore, the correct option is 26.
Important Questions from Properties of Materials
Which of the following statement is incorrect about thermoplastic polymer?
- The point at which a magnetic material loses its ferromagnetic properties is called:
Soft magnetic materials like iron and its alloys are used in the manufacture of:
The main constituent of ferrous metals is:
Which of the following is not a non-ferrous alloy?
