What is an ohm and what is Ohms Law in the cable ?

The ohm (Ω) is the SI unit of electrical resistance. It quantifies how much a material resists the flow of electric current.

Definition: If a voltage of 1 volt causes a current of 1 ampere to flow through a conductor, the resistance of that conductor is 1 ohm.

Formula:
R = V / IWhere:
- R: Resistance in ohms (Ω),
- V: Voltage in volts (V),
- I: Current in amperes (A).

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What is Ohm's Law?

Ohm's Law states the relationship between voltage (V), current (I), and resistance (R) in an electrical circuit:

V = I * R
Where:
- V: Voltage across the conductor (V),
- I: Current flowing through the conductor (A),
- R: Resistance of the conductor (Ω).

Key Points:

• Voltage is directly proportional to current if resistance remains constant.
• Current is inversely proportional to resistance if voltage remains constant.

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Factors Affecting Resistance

• Material: Conductors (e.g., copper) have low resistance, while insulators (e.g., rubber) have high resistance.
• Length (L): Resistance increases with length.
• Cross-Sectional Area (A): Resistance decreases as the area increases.
• Temperature: Resistance increases with temperature for most conductors.

Resistance Formula for a Cable:
R = ρ * (L / A)Where:
- ρ: Resistivity of the material (Ω·m),
- L: Length of the conductor (m),
- A: Cross-sectional area (m²).

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Sample Calculation Using a Cable

Given:

• Cable material: Copper (ρ = 1.68 × 10⁻⁸ Ω·m).
• Cable length (L): 50 m.
• Cross-sectional area (A): 2 mm² (A = 2 × 10⁻⁶ m²).
• Voltage applied (V): 12 V.

Step 1: Calculate the Resistance (R):
R = ρ * (L / A)
R = (1.68 × 10⁻⁸) * (50 / 2 × 10⁻⁶)
R = 0.42 Ω

Step 2: Calculate the Current (I) Using Ohm's Law:
I = V / R
I = 12 / 0.42
I ≈ 28.57 A

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Conclusion

The resistance of the cable is 0.42 Ω, and with an applied voltage of 12 V, the current flowing through the cable is approximately 28.57 A.

This example shows how Ohm's Law and the resistance formula are used to analyze real-world electrical scenarios.