Ohm's Law

Ohm's law is a fundamental principle in physics and electrical engineering that describes the relationship between electric current, voltage, and resistance. It states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points, and inversely proportional to the resistance between them. Mathematically, Ohm's law is expressed as:

I = V / R.

where I is the current flowing through the conductor in amperes (A), V is the voltage across the two points in volts (V), and R is the resistance of the conductor in ohms (Ω). This equation can be rearranged in various ways to solve for different variables depending on what is known and what needs to be calculated

Ohm's law can be derived from basic principles of electrical circuits. Consider a conductor of uniform cross-sectional area A, length L, and resistance R, through which a current I is flowing from point A to point B, with a voltage V applied across the two points. According to the basic principles of electrical circuits, the current flowing through the conductor is proportional to the voltage applied across it and inversely proportional to its resistance. Mathematically, this can be expressed as:

I ∝ V/R

where the symbol ∝ means "is proportional to". To find the constant of proportionality, we can introduce a proportionality factor, which we will call k. Thus, we can write:

I = kV/R

Now, we need to determine the value of k. To do this, we can consider a special case where the conductor is made of a material with a constant resistivity ρ (measured in ohm-meters). In this case, the resistance of the conductor can be expressed as:

R = ρL/A

Substituting this expression into the previous equation, we get:

I = kVρL/A

Now, we can rearrange this equation to isolate the constant of proportionality k:

k = A/(ρL)

Substituting this expression for k back into the earlier equation, we get:

I = V/(ρL/A)

Simplifying the expression on the right-hand side, we get:

I = VA/Lρ

Finally, we can recognize that the quantity A/L is the cross-sectional area per unit length of the conductor, which we will call the conductivity σ (measured in siemens/meter). Thus, we arrive at the familiar form of Ohm's law:

I = V/R = σA V/L

where R is the resistance of the conductor, σ is its conductivity, and A and L are its cross-sectional area and length, respectively.

There are several variations of Ohm's law equations that can be used to calculate different quantities related to electric circuits. The most common equations are:

1. I = V/R: This is the standard form of Ohm's law, where I is the current flowing through a circuit, V is the voltage across the circuit, and R is the resistance of the circuit.

2. V = IR: This equation allows you to calculate the voltage across a circuit given the current flowing through it and the resistance of the circuit.

3. R = V/I: This equation allows you to calculate the resistance of a circuit given the voltage across it and the current flowing through it.

4. P = VI: This equation allows you to calculate the power (in watts) being dissipated by a circuit, where P is the power, V is the voltage, and I is the current.

5. P = V^2/R: This equation allows you to calculate the power being dissipated by a circuit given the voltage and resistance of the circuit.

6. P = I^2R: This equation allows you to calculate the power being dissipated by a circuit given the current flowing through the circuit and the resistance of the circuit.

These equations are all based on the fundamental principle of Ohm's law, which states that the current flowing through a conductor is directly proportional to the voltage across it, and inversely proportional to the resistance of the conductor.