Question

What is the limit of the application of Ohms law and the power formula?

Answer 1

Ohm's Law and the power formula are foundational concepts in electrical engineering, but like any theory, they have certain limitations. Here’s a breakdown of the limits of both:

1. Limitations of Ohm's Law

Ohm’s Law states that \( V = I \times R \), where:

1. \( V \) is the voltage across the resistor,
   

1. \( I \) is the current passing through the resistor,
   

1. \( R \) is the resistance of the resistor.
   

However, Ohm’s Law applies only to linear, resistive materials. It breaks down in the following scenarios:

1. Non-linear materials: For example, materials like semiconductors (e.g., diodes or transistors), which do not follow the linear relationship between voltage and current, cannot be described by Ohm's Law.
   

  

1. High-frequency signals: When alternating current (AC) is applied at very high frequencies, reactive elements like inductors and capacitors start affecting the circuit. These elements introduce reactance, which means the relationship between voltage and current is no longer governed purely by resistance (i.e., the impedance comes into play, which changes with frequency).
   

1. Very high voltages or currents: At extreme levels of voltage or current, the material properties of the resistor can change (for example, heating or breakdown of the material), causing the resistance to vary. This results in Ohm's Law no longer being valid because the relationship between current and voltage becomes non-linear.
   

1. Superconductors: At extremely low temperatures, superconductors exhibit zero resistance, meaning Ohm's Law doesn’t apply in the traditional sense because the resistance term \( R \) becomes 0, leading to infinite current for any applied voltage.
   

2. Limitations of the Power Formula

The power formula is usually given as:
\[ P = V \times I \]
where:

1. \( P \) is power,
   

1. \( V \) is voltage,
   

1. \( I \) is current.
   

This formula assumes that both the voltage and the current are constant or DC values. However, when it comes to AC circuits or circuits with reactive elements (inductors and capacitors), the formula must be modified.

1. AC circuits with reactive components: In AC circuits, power calculation involves both real power and reactive power. The real power is the actual power consumed by the load, while the reactive power represents the energy alternately stored and released by inductors and capacitors. The formula becomes:
   

  \[
  P_{avg} = V_{rms} \times I_{rms} \times \cos(\phi)
  \]
  where \( \phi \) is the phase difference between the voltage and current. Here, \( \cos(\phi) \) is called the power factor, which accounts for the difference in phase.

1. Non-sinusoidal waveforms: The basic formula \( P = V \times I \) is simplified for pure sinusoidal AC waveforms. If the waveform is distorted (e.g., in the presence of harmonics), the power calculation becomes more complex, often requiring the use of the Fourier series to break the waveform down into its components.
   

1. Power losses: The simple power formula doesn't account for energy losses due to resistance, inductive or capacitive reactance, or other non-ideal factors. So in practical circuits, power losses and efficiency need to be considered to understand the real power consumption.
   

Summary of the Limitations:

1. Ohm's Law: Does not apply to non-linear components, high-frequency signals, extreme voltage/current conditions, or superconductors.
   

1. Power Formula: Needs adjustment for AC circuits, reactive power, non-sinusoidal signals, and power losses.
   

In essence, while these formulas are useful for many everyday electrical problems, they don't cover the complexity of more advanced or non-ideal scenarios.