The Formula for Temperature Coefficient of Resistance

Oct 13, 2025 by vinooalluri.com 141 views

**To Increase the Resistance of a Wire by 15%: Understanding the Relationship Between Temperature and Resistance**

What is the Relationship Between Temperature and Resistance?

The relationship between temperature and resistance is a fundamental concept in physics, particularly in the study of electrical properties of materials. As the temperature of a wire increases, its resistance also increases. This is due to the thermal motion of the atoms or molecules in the wire, which causes the electrons to collide more frequently with the atoms, resulting in a decrease in the flow of electric current.

The Formula for Temperature Coefficient of Resistance

The temperature coefficient of resistance (α) is a measure of how much the resistance of a material changes with temperature. It is defined as the change in resistance per unit change in temperature. The formula for the temperature coefficient of resistance is:

α = (R₂ - R₁) / (T₂ - T₁)

where R₁ and R₂ are the resistances at temperatures T₁ and T₂, respectively.

Calculating the Final Temperature

To calculate the final temperature of the wire, we need to use the formula for the temperature coefficient of resistance. We are given that the initial temperature of the wire is 30°C and that we want to increase its resistance by 15%. We are also given the value of α, which is 6.81 x 10⁻³ °C⁻¹.

Let's assume that the initial resistance of the wire is R₁ and the final resistance is R₂. We can write the equation for the change in resistance as:

R₂ = R₁ + (15% of R₁)

We can simplify this equation to:

R₂ = 1.15R₁

Now, we can use the formula for the temperature coefficient of resistance to calculate the final temperature:

α = (R₂ - R₁) / (T₂ - T₁)

Substituting the values, we get:

6.81 x 10⁻³ = (1.15R₁ - R₁) / (T₂ - 30)

Simplifying the equation, we get:

6.81 x 10⁻³ = 0.15R₁ / (T₂ - 30)

Now, we can solve for T₂:

T₂ - 30 = 0.15R₁ / (6.81 x 10⁻³)

T₂ = 30 + (0.15R₁ / (6.81 x 10⁻³))

Calculating the Final Temperature

To calculate the final temperature, we need to know the value of R₁. However, we are not given the value of R₁. We can assume a value for R₁ and calculate the final temperature.

Let's assume that the initial resistance of the wire is 10 Ω. We can substitute this value into the equation:

T₂ = 30 + (0.15 x 10) / (6.81 x 10⁻³)

T₂ = 30 + 2.22

T₂ = 32.22°C

Therefore, the final temperature of the wire is approximately 32.22°C.

Q&A

Q: What is the relationship between temperature and resistance?

A: The relationship between temperature and resistance is that as the temperature of a wire increases, its resistance also increases.

Q: What is the formula for the temperature coefficient of resistance?

A: The formula for the temperature coefficient of resistance is:

α = (R₂ - R₁) / (T₂ - T₁)

Q: How do I calculate the final temperature of a wire?

A: To calculate the final temperature of a wire, you need to use the formula for the temperature coefficient of resistance and substitute the values of R₁, R₂, and α.

Q: What is the value of α for a wire?

A: The value of α for a wire is 6.81 x 10⁻³ °C⁻¹.

Q: How much should I raise the temperature of a wire to increase its resistance by 15%?

A: To increase the resistance of a wire by 15%, you should raise its temperature by approximately 2.22°C.

Q: What is the final temperature of a wire if its initial temperature is 30°C and its resistance is increased by 15%?

A: The final temperature of a wire if its initial temperature is 30°C and its resistance is increased by 15% is approximately 32.22°C.

Conclusion

In conclusion, the relationship between temperature and resistance is a fundamental concept in physics. The temperature coefficient of resistance is a measure of how much the resistance of a material changes with temperature. By using the formula for the temperature coefficient of resistance, we can calculate the final temperature of a wire if its initial temperature and resistance are known. In this article, we calculated the final temperature of a wire if its initial temperature is 30°C and its resistance is increased by 15%.