Calculate the power is dissipated in a 80m length of cable that has a resistance of 0.003ohms per metre if a current of 10amps flows through it 

To calculate the power dissipated in the cable, we can use the following formula based on Joule's law of heating:

\[
P = I^2 \cdot R
\]

Where:
- \(P\) is the power dissipated (in watts, W),
- \(I\) is the current (in amperes, A),
- \(R\) is the total resistance of the cable (in ohms, \(\Omega\)).

First, we need to calculate the total resistance of the cable:

\[
R = \text{Resistance per metre} \times \text{Length of the cable}
\]
\[
R = 0.003 \, \Omega/\text{m} \times 80 \, \text{m} = 0.24 \, \Omega
\]

Now, use the formula for power dissipation:

\[
P = 10^2 \times 0.24 = 100 \times 0.24 = 24 \, \text{W}
\]

Thus, the power dissipated in the cable is **24 watts**.

Do you want more details or have any questions about this?

Here are 5 related questions for further exploration:
1. How does the power dissipation change if the current increases to 15 A?
2. What would be the total resistance for a cable that is 100 meters long?
3. How much energy would be dissipated over 1 hour of continuous current flow?
4. How does reducing the cable length affect the power dissipated?
5. What is the effect of using a cable with higher resistance per meter?

**Tip:** Power dissipation increases with the square of the current, meaning a small increase in current results in a significant increase in power loss.

Calculate the power dissipated in an 80m length of cable that has a resistance of 0.003 ohms per metre if a current of 10 amps flows through it.

Learn how to calculate the power dissipated in an 80-meter long cable with a resistance of 0.003 ohms per meter and a current of 10 amps. Using Ohm's Law and Joule's Law of Heating, this problem covers key physics concepts and provides a detailed step-by-step solution. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation