a 5*C rise in temperature is observed in a conductor by passing some current.when the current is doubled,then rise in temperature will be equal to

To understand how the temperature rise in a conductor relates to the current passing through it, we can use some principles of physics, particularly those related to electrical resistance and heating effects. When current flows through a conductor, it generates heat due to the resistance of the material. The amount of heat produced is proportional to the square of the current, according to Joule's law.

Joule's Law and Heat Generation

Joule's law states that the heat (Q) produced in a conductor is given by the formula:

• Q = I² * R * t

Where:

• Q = heat generated
• I = current
• R = resistance of the conductor
• t = time for which the current flows

Understanding the Initial Temperature Rise

In your scenario, a current results in a temperature rise of 5°C. Let's denote the initial current as I. According to Joule's law, the heat generated (and thus the temperature rise) when the current is I can be expressed as:

• ΔT1 = k * I²

Here, ΔT1 is the temperature rise (5°C), and k is a constant that depends on the resistance and time. This means:

• 5 = k * I²

Doubling the Current

Now, when the current is doubled to 2I, we can find the new temperature rise (ΔT2) using the same relationship:

• ΔT2 = k * (2I)²

Expanding this gives:

• ΔT2 = k * 4I²

Since we know from the earlier calculation that k * I² = 5, we can substitute this back into the equation:

• ΔT2 = 4 * (k * I²) = 4 * 5 = 20°C

Final Thoughts

Thus, when the current is doubled, the rise in temperature will be equal to 20°C. This illustrates a fundamental concept in physics: the relationship between current and heat generation in conductors is quadratic, meaning that even a small increase in current can lead to a significant increase in temperature.

Dear Student,
Please find below the solution to your problem.

Thanks and Regards