a coil consist of 1000 turns of copper wire having a cross- sectional area of 0.8mm^2.the mean length is 0.02μΩm. find the resistance of the coil 110V d.c supply.

To calculate the resistance of the coil, we can use the following formula:

\[
R = \rho \cdot \frac{L}{A}
\]

where:
- \( R \) is the resistance of the coil.
- \( \rho \) is the resistivity of copper.
- \( L \) is the length of the wire.
- \( A \) is the cross-sectional area of the wire.

Given:
- Number of turns = 1000
- Cross-sectional area \( A = 0.8 \, \text{mm}^2 = 0.8 \times 10^{-6} \, \text{m}^2 \)
- Mean length per turn \( L_{\text{mean}} = 0.02 \, \mu\Omega \text{m} = 0.02 \times 10^{-6} \, \Omega \text{m} \)
- Resistivity of copper \( \rho \approx 1.68 \times 10^{-8} \, \Omega \text{m} \)

The total length \( L \) of the wire will be:

\[
L = 1000 \times L_{\text{mean}}
\]

Now, let's calculate the resistance.

1. **Total length of the wire:**

\[
L = 1000 \times 0.02 \times 10^{-6} \, \Omega \text{m} = 2 \times 10^{-5} \, \Omega \text{m}
\]

2. **Calculate the resistance:**

\[
R = \rho \cdot \frac{L}{A} = 1.68 \times 10^{-8} \, \Omega \text{m} \cdot \frac{2 \times 10^{-5} \, \Omega \text{m}}{0.8 \times 10^{-6} \, \text{m}^2}
\]

\[
R = 4.2 \times 10^{-7} \, \Omega
\]

Thus, the resistance of the coil is approximately \(4.2 \times 10^{-7} \, \Omega\).

Would you like more details or have any questions about this problem?

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Here are 5 related questions you might find interesting:
1. How would the resistance change if the cross-sectional area of the wire were doubled?
2. What effect would using a different material with higher resistivity have on the coil's resistance?
3. How would the resistance be affected if the coil had only 500 turns instead of 1000?
4. Can you calculate the power dissipated in the coil when connected to the 110V DC supply?
5. How does the length of the wire influence the resistance in general?

**Tip:** In electrical circuits, resistance is a crucial factor in determining how much current flows for a given voltage. Always check both material and geometry when calculating resistance.

Learn how to calculate the resistance of a copper coil consisting of 1000 turns with a cross-sectional area of 0.8mm^2. Detailed step-by-step solution using Ohm's Law and copper's resistivity. Suitable for high school students studying electrical circuits.

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