Tungsten Wire Current: Temperature's Impact

Hey guys! Let's dive into a fascinating physics problem. We're going to explore how temperature affects the current flowing through a tungsten wire. Specifically, we'll figure out how much more current will flow at room temperature compared to when the wire is heated up to a scorching 1000°C. This is super important for understanding how electrical circuits behave under different conditions, and it's a great example of applying basic physics principles. So, grab your calculators, and let's get started!

Understanding the Problem: Unveiling the Core Concepts

Alright, so here's the deal. We have a tungsten wire that's pretty thin – only 0.010 inches in diameter and 15 feet long. We're going to hook it up to a constant 50-volt power supply. The main question is: how does the current flowing through this wire change as its temperature changes? At room temperature, the wire will have a specific resistance. When we heat the wire up to 1000°C, its resistance will change. This change in resistance, due to temperature, directly impacts the current. This is because, according to Ohm's Law (V = IR, where V is voltage, I is current, and R is resistance), the current is inversely proportional to the resistance when the voltage is constant. So, if the resistance goes up, the current goes down, and vice versa.

The key here is understanding how temperature affects the resistance of a metal. Generally, the resistance of a metal increases with temperature. This is because the atoms in the wire vibrate more vigorously at higher temperatures, making it harder for the electrons (which carry the current) to move through the wire. These collisions between the electrons and the vibrating atoms hinder the flow of current, increasing the resistance. Tungsten is a great example of a material that exhibits this behavior. This property is super important in practical applications, like light bulbs, where the tungsten filament heats up and glows, providing light. So, the higher the temperature, the greater the resistance, and therefore, the lower the current, given a constant voltage source. So let's start by breaking down this problem into steps.

Calculating Resistance: The Foundation of Our Analysis

Before we can compare the currents at different temperatures, we need to figure out the resistance of the tungsten wire at both room temperature and 1000°C. Let's start with the basics. The resistance of a wire can be calculated using the following formula:

R = (ρ * L) / A

Where:

• R is the resistance of the wire (in ohms, Ω).
• ρ is the resistivity of the material (in ohm-meters, Ω·m).
• L is the length of the wire (in meters, m).
• A is the cross-sectional area of the wire (in square meters, m²).

So, we will need the resistivity of tungsten at room temperature and 1000°C, the length and the cross-sectional area. Let's find those values. The length of the wire is given as 15 feet, which we need to convert to meters (1 foot = 0.3048 meters).

L = 15 ft * 0.3048 m/ft = 4.572 m

The diameter of the wire is 0.010 inches, which we also need to convert to meters (1 inch = 0.0254 meters).

diameter = 0.010 in * 0.0254 m/in = 0.000254 m

Now, we need to calculate the cross-sectional area of the wire. Since the wire is cylindrical, the cross-sectional area (A) is a circle, and the area of a circle is given by:

A = π * (d/2)^2

Where d is the diameter. So,

A = π * (0.000254 m / 2)^2 = 5.067 * 10^-8 m^2

Now we can use the resistivity of tungsten. The resistivity of tungsten at room temperature (approximately 20°C) is about 5.6 x 10^-8 Ω·m. The resistivity of tungsten at 1000°C is approximately 7.6 x 10^-7 Ω·m. Now, let's calculate the resistance at room temperature.

R_room = (5.6 * 10^-8 Ω·m * 4.572 m) / 5.067 * 10^-8 m^2 = 5.04 Ω

Now, at 1000°C:

R_1000 = (7.6 * 10^-7 Ω·m * 4.572 m) / 5.067 * 10^-8 m^2 = 68.46 Ω

So, the resistance goes up quite a bit as the temperature increases!

Determining the Current: Applying Ohm's Law

Now that we have the resistances, we can use Ohm's Law (V = IR) to calculate the current at each temperature. Remember, our voltage is a constant 50 V. We can rearrange Ohm's Law to solve for current (I = V/R).

At room temperature:

I_room = 50 V / 5.04 Ω = 9.92 A

At 1000°C:

I_1000 = 50 V / 68.46 Ω = 0.73 A

The Final Comparison: Revealing the Difference

Okay, we've got the current at both temperatures! At room temperature, the current is approximately 9.92 Amperes. At 1000°C, the current is approximately 0.73 Amperes. To find out how much more current is conducted at room temperature, we simply subtract the current at 1000°C from the current at room temperature:

ΔI = I_room - I_1000 = 9.92 A - 0.73 A = 9.19 A

So, the wire conducts about 9.19 Amperes more current at room temperature than at 1000°C. This is a significant difference, highlighting how much the change in resistance due to temperature affects the current flow.

Conclusion: Temperature and Current – A Powerful Combination

In a nutshell: We've successfully navigated this physics problem! We started with a tungsten wire, calculated its resistance at different temperatures, and then used Ohm's Law to determine the current flowing through the wire under a constant voltage. We found that the current significantly decreases as the temperature of the wire increases. This is because the increased temperature causes more resistance. This experiment gives us a better grasp of how temperature affects the electrical properties of materials. This understanding is fundamental in electronics and other areas of physics. Understanding concepts like these is crucial in a ton of applications, from designing light bulbs to understanding how electronic circuits behave under different conditions. Keep exploring, keep questioning, and always keep learning! Until next time, stay curious and keep the physics fun alive! If you have any questions, feel free to ask!