Ohm's Law and Resistance

1. Ohm's Law

Ohm's Law is a fundamental principle in electrical engineering that describes the relationship between voltage (V), current (I), and resistance (R) in an electrical circuit. The law is expressed mathematically as:

V = I × R

Where:

V is the voltage across the conductor, measured in volts (V).
I is the current through the conductor, measured in amperes (A).
R is the resistance of the conductor, measured in ohms (Ω).

Example: If a circuit has a resistance of 10 ohms and a current of 2 amperes flowing through it, the voltage across the circuit can be calculated as:

V = I × R = 2 A × 10 Ω = 20 V

2. Resistance

Resistance is the property of a material that opposes the flow of electric current. It is measured in ohms (Ω). High resistance means that a material resists the flow of current, while low resistance allows current to flow more easily.

Resistance (R) in a conductor depends on several factors:

Length (L): Longer conductors have higher resistance.
Cross-sectional area (A): Wider conductors have lower resistance.
Material: Different materials have different resistivities (ρ).

The relationship can be expressed as:

R = ρ × (L / A)

Example: If a copper wire has a length of 5 meters and a cross-sectional area of 0.0001 square meters, and the resistivity of copper is 1.72 × 10^-8 Ω·m, the resistance can be calculated as:

R = ρ × (L / A) = 1.72 × 10^-8 Ω·m × (5 m / 0.0001 m²) = 0.086 Ω

3. Practical Applications

Understanding Ohm's Law and resistance is crucial in designing and troubleshooting electrical circuits. For instance, in designing a circuit, engineers must ensure that the components can handle the expected current without overheating.

Example: In a simple flashlight circuit, the battery provides a voltage, and the bulb acts as a resistor. By knowing the voltage of the battery and the resistance of the bulb, you can calculate the current flowing through the circuit using Ohm's Law.

4. Series and Parallel Circuits

In series circuits, the total resistance is the sum of individual resistances. In parallel circuits, the reciprocal of the total resistance is the sum of the reciprocals of individual resistances.

Example: If two resistors of 10 ohms each are connected in series, the total resistance is 20 ohms. If they are connected in parallel, the total resistance is:

1/R_total = 1/R₁ + 1/R₂ = 1/10 + 1/10 = 2/10 = 0.2

R_total = 1 / 0.2 = 5 ohms