Voltage, current, and resistance relationship

Voltage (V), current (I), and resistance (R) are three fundamental quantities in electrical circuits. They are related to each other through Ohm’s law, which 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 can be expressed as:

V = I * R

where V is the voltage in volts, I is the current in amperes, and R is the resistance in ohms.

In other words, the voltage is equal to the product of the current and the resistance. This means that if the voltage is increased, the current will increase if the resistance remains constant, and if the resistance is increased, the current will decrease if the voltage remains constant.

Ohm’s law can also be used to calculate any one of the three quantities if the other two are known. For example, if the voltage and resistance are known, the current can be calculated using the formula:

I = V / R

Similarly, if the current and resistance are known, the voltage can be calculated using the formula:

V = I * R

The relationship between voltage, current, and resistance is crucial to understanding how electrical circuits work, and is fundamental to many aspects of electrical engineering and physics.

Ohm’s law states that the R in this relation is constant and independent of the current. If the resistance is not constant, the previous equation cannot be called Ohm’s law, but it can still be used as a definition of static/DC resistance. Ohm’s law is an empirical relation that accurately describes the conductivity of the vast majority of electrically conductive materials over many orders of magnitude of the current. However, some materials do not obey Ohm’s law; these are called non-ohmic.

Application of Ohm’s law

Ohm’s law is a fundamental principle of electrical engineering and is used in many practical applications. Here are a few examples:

  1. Circuit design: Ohm’s law is used extensively in the design of electrical circuits, where it helps engineers to determine the proper values of resistors, capacitors, and other components needed to achieve the desired current and voltage levels.
  2. Electrical safety: Ohm’s law is also used in the design of electrical safety systems, such as fuses and circuit breakers. These devices are designed to break the circuit when the current exceeds a certain level, which is determined by the resistance of the circuit.
  3. Power distribution: Ohm’s law is used to calculate the power dissipated in a circuit, which is important for power distribution systems. By knowing the voltage and current of a circuit, engineers can calculate the power consumed by the circuit and determine the proper size of wires, transformers, and other components needed for efficient power distribution.
  4. Electronics troubleshooting: Ohm’s law is also used in troubleshooting electrical problems in electronic devices. By measuring the voltage and current of a circuit, engineers can determine the resistance of the circuit and identify any faulty components or connections that may be causing problems.

Overall, Ohm’s law is a critical concept in electrical engineering and is used in a wide range of applications, from basic circuit design to complex power distribution systems.

Theory of Ohm’s law

Ohm’s law can be explained at a microscopic level by understanding the behavior of electrons in a conductor.

In a conductor, such as a metal wire, there are free electrons that are able to move through the material. These electrons collide with the atoms of the conductor as they move, which creates a resistance to their motion. The resistance of a conductor is related to the number of collisions that occur as electrons move through it.

When a voltage is applied across a conductor, it creates an electric field that causes the free electrons to move in a particular direction. The electrons experience a force due to this electric field, which causes them to accelerate and move through the conductor. However, the electrons do not move in a straight line but rather undergo a random motion due to collisions with the atoms of the conductor, losing energy and scattering in random directions. This creates resistance to the flow of electrons and causes some of the energy of the electric field to be converted into heat.

Ohm’s law can be understood in terms of this electron behavior. The current through a conductor is directly proportional to the voltage applied across it, because a higher voltage creates a stronger electric field that causes the electrons to move faster, resulting in a higher current. However, the current is inversely proportional to the resistance of the conductor, because a higher resistance means that there are more collisions and, therefore fewer free electrons available to carry the current.

Thus, Ohm’s law can be understood as a balance between the forces driving the electrons (the electric field) and the forces resisting their motion (collisions with atoms), resulting in a relationship between the current, voltage, and resistance of a conductor.

The drift velocity of electrons in a conductor is typically quite slow, on the order of a few millimeters per second, even though the current in the conductor may be quite high. This is because the electrons are constantly colliding with the atoms of the conductor, which slows down their overall motion. Drift velocity is proportional to current. In a resistive material, it is also proportional to the magnitude of an external electric field.

While the drift velocity is relatively slow, it is still an important concept in understanding the behavior of electric currents in conductors. The overall flow of electric charge in a conductor is determined by the combination of the drift velocity and the number of charge carriers moving through the conductor.

For example, when a DC voltage is applied, the electron drift velocity will increase in speed proportionally to the strength of the electric field. The drift velocity in a 2 mm diameter copper wire in 1 ampere current is approximately 8 cm per hour. AC voltages cause no net movement; the electrons oscillate back and forth in response to the alternating electric field (over a distance of a few micrometers).

Ohm’s law – Hydraulic Analogy

The hydraulic analogy, or the electric-fluid analogy, is a widely used analogy between hydraulics and electricity, which is a useful tool for teaching and for those who are struggling to understand how circuits work. it can also be applied to heat transfer problems. 

Since electric current is invisible and the processes in play in electronics are often difficult to demonstrate, the various electronic components are represented by hydraulic equivalents. The relationship between voltage and current is defined (in ohmic devices like resistors) by Ohm’s law. Ohm’s Law is analogous to the Hagen–Poiseuille equation, as both are linear models relating flux and potential in their respective systems.

Electricity (as well as heat) was originally understood to be a kind of fluid, and the names of certain electric quantities (such as current) are derived from hydraulic equivalents.

  • Voltage is like the pressure difference that pushes water through the hose. It is measured in volts (V). This model assumes that the water is flowing horizontally so that the force of gravity can be ignored.
  • Current is equivalent to a hydraulic volume flow rate; that is, the volumetric quantity of flowing water over time. Usually measured in amperes. The wider pipe is, the more water will flow through. It is measured in amps (I or A).
  • Resistance is like pipe diameter or obstacles in the hose that slow down the water flow. It is measured in ohms (Ω). In hydraulics, resistance is associated with the pressure loss coefficient.
  • Resistors are comparable to a section of the pipe network where the radius of the pipe is constricted, restricting the rate of fluid flow in that region, the same way that a resistor limits current.

Examples of Ohm’s law

Here are two examples of calculations using Ohm’s law:

Example 1: Suppose a circuit has a resistance of 10 ohms and a voltage of 20 volts. To calculate the current through the circuit using Ohm’s law, we can use the formula:

I = V / R

where I is the current, V is the voltage, and R is the resistance.

Plugging in the values, we get:

I = 20 V / 10 Ω = 2 A

Therefore, the current through the circuit is 2 amperes.

Example 2: Suppose a circuit has a current of 0.5 amperes and a resistance of 100 ohms. To calculate the voltage across the circuit using Ohm’s law, we can use the formula:

V = I x R

where V is the voltage, I is the current, and R is the resistance.

Plugging in the values, we get:

V = 0.5 A x 100 Ω = 50 V

Therefore, the voltage across the circuit is 50 volts.

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