1. Introduction

2. Evaluating the Evolution of Efforts to Contest the Law of Energy Conservation

3. Breaking the Law of Energy Conservation

3.2. Design of the Proposed Energy Circuit (The Main Energy Circuit Operational Units)

This section describes the key components and design considerations of the energy circuit. It also offers the specific energy circuit units mathematical framework defining the necessary energy circuit ingredients, and their uses.

3.2.1. Circuit Component 1 (Power Source): The energy circuit begins with a power supply (for safety check, a direct voltage and direct current power source is selected). This power source (variable power supply or using different rating power sources may be considered, as applied in this paper) represents the starting point of the energy conservation challenge. Details on the starting current, the connecting codes (conductors) practical resistance (and conductors material types) will be of importance in working out the input power for the subsequent circuit blocks, modeling the real world scenarios.

Initial Exploration of Ohm’s Law (“Circuit Block 1”): This initial section of the energy circuit deviates from the traditional approach of demonstrating standard Ohm’s Law ($V=IR$) that characterizes traditional electrical circuits. Instead, “Circuit Block 1” primarily aims to use two identical one-directional current components in a parallel configuration (as shown in Figure 1), to prevent undesired electrical current from flowing back. First, let us set up the mathematical framework for “Circuit Block 1” using the diode equation, (equation 1) as applied in [52,53]. Thus, the current-voltage (IV) relationship for a diode is described by the diode equation as follows.

$$I_D=I_s\left(e^{\left(\raisebox{1ex}{$V_D$}\!\left/ \!\raisebox{-1ex}{$n{V}_T$}\right.\right)}-1\right)$$

(1)

where:

• $I_D$  is the diode current.
• $I_s$ ​ is the reverse saturation current.
• $V_D$  is the voltage across the diode.
• $n$ is the ideality factor (typically around $1$ for ideal diodes).
• $V_T$ is the thermal voltage, approximately $0.0259V$ at room temperature.

Since the diodes are in parallel, the total current through “Circuit Block 1” (denoted as $I_{CB1}$​) is the sum of the currents through each diode. Therefore, for two diodes ($D_1$ and $D_2$ as depicted in (figure 1)) in parallel we have;

$$I_{CB1}=I_{D_1}+I_{D_2}$$

(2)

Substituting the diode equation for this parallel diodes configuration;

$$I_{CB1}=I_s\left(e^{\left(\raisebox{1ex}{$V_{D_1}$}\!\left/ \!\raisebox{-1ex}{$n{V}_T$}\right.\right)}-1\right)+I_s\left(e^{\left(\raisebox{1ex}{$V_{D_2}$}\!\left/ \!\raisebox{-1ex}{$n{V}_T$}\right.\right)}-1\right)$$

(3)

Combining the like terms in equation (3) and factoring out $I_s$​ we get;

$$I_{CB1}=I_s\left[e^{\left(\raisebox{1ex}{$V_{D_1}$}\!\left/ \!\raisebox{-1ex}{$n{V}_T$}\right.\right)}+e^{\left(\raisebox{1ex}{$V_{D_2}$}\!\left/ \!\raisebox{-1ex}{$n{V}_T$}\right.\right)}-2\right]$$

(4)

Equation (4) represents the total current flowing through the diodes in the parallel configuration. Further, the voltage across “Circuit Block 1” (denoted as $V_{CB1}$) can be expressed as;

$$V_{CB1}=V_{D_1}+V_{D_2}$$

(5)

To use equation (4); one is required to have the specific voltage values ($V_{D_1}$, and $V_{D_2}$), ideality factor ($n$), and reverse saturation current ($I_s$), for the different identical diodes to be applied in the circuit. In this context, the main role for “Circuit Block 1” is to inhibit current from returning to the power source, which is vital for ensuring the overall integrity of the following energy circuit stages. The subsequent stage, “Circuit Block 2”, introduces the concept of an electrical short circuit, a design that relies on the availability of a surplus of electrical current. Allowing the short circuit current to return to the power source could potentially harm the source. The effectiveness of “Circuit Block 1” in preventing backflow relies on the initial power supplied from the variable power supply component. Consequently, the selection of the specific one-directional current components used within “Circuit Block 1” may vary based on the circuit application’s power requirements. Further, it is important to stress that these one-directional current components are not fixed and can be adapted to the unique characteristics of each application, contributing to the energy circuit’s versatility.

3.2.2. Operation Principles of “Circuit Block 1” (Establishing Higher Resistive Circuit Element)

The crucial role of “Circuit Block 1” is to prevent the undesired backflow of short circuit current from “Circuit Block 2”. Its operation involves an uncommon configuration with parallel diodes, hindering the reverse flow of current. When the short circuit current tries to move backward, it forces the diodes into a reverse-biased mode, causing their depletion regions to widen. This widening of the depletion regions increases the resistance in “Circuit Block 1”, serving as a barrier and limiting the ability of the short circuit current (this current is quantifiable as worked out using equation (6)) to flow backward through the diodes.

Definition 1 (Diode Idle State or Mode):

This definition contextualizes a reverse-biased diode as active but not conducting (a diode set at $0V$from the source), and it only conducts in reverse bias mode when the anomalous event (the electrical short circuit) occurs within an electric circuit. In Figure 1, $D_2$is in the idle state or mode, becoming an infinite resistor (theoretically) when the short circuit happens.

Figure 1. Operational Principle of “Circuit Block 1”-Diode Configuration. (The diodes ($D_1$ and $D_2$) are configured in parallel with the specific arrangement to prevent undesired backflow of short circuit current from “Circuit Block 2”. As the short circuit current attempts to flow in reverse, the diodes transition to a reverse-biased mode, widening the depletion region and increasing resistance, acting as a barrier to the reverse flow. The block diagram illustrates the parallel connection of diodes).

Figure 1. Operational Principle of “Circuit Block 1”-Diode Configuration. (The diodes ($D_1$ and $D_2$) are configured in parallel with the specific arrangement to prevent undesired backflow of short circuit current from “Circuit Block 2”. As the short circuit current attempts to flow in reverse, the diodes transition to a reverse-biased mode, widening the depletion region and increasing resistance, acting as a barrier to the reverse flow. The block diagram illustrates the parallel connection of diodes).

3.3. Harnessing the Short Circuit Power (“Circuit Block 2”)

The “Circuit Block 2” serves as an extension of the preceding stage, “Circuit Block 1”, directly receiving the current and voltage output from “Circuit Block 1”. As shown in Figure 2, a resistive element, which may be symbolized by a high-value resistor, is connected between the positive output terminal (labeled $A$) and the negative output terminal (labeled $B$) of “Circuit Block 1”. This connection introduces an electrical short circuit, fundamentally altering the energy dynamics within the circuit, facilitating exceptional energy conservation and utilization as demonstrated later.

3.3.1. Description of “Circuit Block 2” Components

Initial State (“Circuit Block 1”): Initially, Diode $D_1$ is forward-biased, being connected to the positive terminal of the voltage source. This allows current to flow through $D_1$ from its anode to cathode. Simultaneously, Diode $D_2$ is reverse-biased as it is connected to the negative terminal of the source, preventing significant current flow through it.

Short Circuit (“Circuit Block 2”)-Current Flow, Voltage Drop and After Short Circuit Event: Upon the creation of a short circuit by connecting points $A$ and $B$, a sudden surge of current traverses the short circuit, causing a momentary voltage drop across both diodes. The short circuit current and voltage has always been experimentally determined, with the short circuit events (current surge and voltage drop) reported in [54,55]). During this transient phase, $D_1$, initially forward-biased, experiences a reversal of voltage polarity. The voltage at point $A$ becomes lower than that at the cathode, prompting $D_1$ to enter a state of reverse bias. This causes the depletion layer to widen as electrons migrate away from the junction. Concurrently, $D_2$, which was in a state of reverse bias from the outset, continues to be reverse-biased even after the short circuit. The voltage at point $B$ remains higher than at the anode (since the anode is initially connected to the power source negative terminals, with $0V$ (the $0V$ voltage is theoretically assumed here)), sustaining the widened depletion layer in $D_2$. The widened depletion layers in both diodes play a pivotal role in controlling the flow of charge carriers, influencing the circuit’s behavior during transient events.

Remark 2 (Circuit Protection Mechanism)

: The protective nature of “Circuit Block 1” lies in the fact that, post short circuit, both diodes are in a state of reverse bias. This configuration impedes the flow of current in the reverse direction, safeguarding the source from potential damage. The depletion layers in $D_1$

and $D_2$act as barriers, restricting the movement of charge carriers and effectively isolating the circuit from any adverse effects caused by the short circuit.

The short circuit current here (named as $shortcircuiteffectcurrent$) is computed using the Ohm’s law modified formula that is designed for use in scenarios including low resistance applications provided by [56], and this current is expressed according to equation (6). Thus, equation (6) provides one of the important ingredients required to compute the electrical short circuit in the energy circuit, as the standard Ohm’s law will not be applicable is such settings.

$$I_{short\mathrm{}circuit\mathrm{}effect\mathrm{}current}=a\times e^{\frac{R_{short}}{R_0}}$$

(6)

Where:

$a=\frac{V}{{\mathrm{R}}_0}$, is current scaling factor.

$R_0$ is the reference resistance.

$V$ is the source or supply voltage.

$R_{short}$ is the change in resistance from its reference value $\left(R_0\right)$.

In this context, $R_{short}=R\left(x\right)-R_0$, and the details on parameter $x$ have been established at (Appendix I) by [56].

Using equations (5) and (6), the power input to “Circuit Block 2” can then be computed following equation (7).

$$P_{{input}_{CB2}}=V_{CB1}\times I_{short\mathrm{}circuit\mathrm{}effect\mathrm{}current}$$

(7)

The primary objectives of “Circuit Block 2” are two-fold. It focuses on generating excess short circuit current and effectively channeling this high current to the subsequent stages of the circuit. The high-value resistor (the resistive element shown in Figure 2), often termed the resistive element, plays a pivotal role in achieving these goals. It not only establishes the short circuit in tandem with “Circuit Block 1” but also ensures the high short circuit current flows forward in the circuit without causing damage. In the essence, this resistive element becomes the first path of low resistance after the electrical short circuit, preventing the excess current from finding its way back. This dual role is crucial, as the resistor, in collaboration with “Circuit Block 1”, prevents undesired backflow, while its high resistance directs the abundant short circuit current toward the next stages. The resistance of the resistive element can be varied by considering the overall resistance of the subsequent circuits to ensure that it is higher (for practical applications, this resistance can be determined based on the computed $I_{shortcircuiteffectcurrent}$), ensuring a forward flow of current and enhancing the overall efficiency and safety of the energy circuit. Importantly, “Circuit Block 1” current and voltage outputs transition to become the inputs for “Circuit Block 2”, maintaining the uninterrupted flow of power and energy throughout the circuit’s progression.

Further, it is imperative to take into account the effective resistance in the “Circuit Block 2”. This resistance will include the overall resistance in “Circuit Block 1”, and it can be computed following equation (8).

$$R_{shorteffective}=R_{{CB1}_{overall}}$$

(8)

It will then be considered that the combined resistance (named subsequently as $R_{forwardcurrent}$) between $R_{shorteffective}$ and the resistance due to the high resistive component facilitating the short circuit also contributes into ensuring the forward current flow, from “Circuit Block 2”. For practical purposes, we will express this resistance following equation (9).

$$R_{forward\mathrm{}current}=R_{short\mathrm{}effective}+R_{resistor}\left(this\mathrm{}could\mathrm{}be\mathrm{}some\mathrm{}value\right)$$

(9)

Here, $R_{resistor}$ is the resistive element resistance. Emphatically, understanding the value ($R_{forwardcurrent}$) is important, mainly because of the major role played by the resistive element in the energy circuit (ensuring that the resistive element is not easily damaged by the excess short circuit current, whenever this resistive element becomes the path of low resistance, from “Circuit Block 1”). There will be solely no other main reasons to compute the ($R_{forwardcurrent}$), besides this.

Then, consider that after the short circuit happens (this event should be time depended as described in “Circuit Block 5”) the input voltage into “Circuit Block 2” is expected to drop suddenly (as earlier established), to some value by some factor (let this factor be named $F_{shortcircuit}$ and for computational and simulation purposes here, it is set to the lowest say $F_{shortcircuit}=0.8$). The $F_{shortcircuit}$ means that the voltage drop after the short circuit is $80\%$ of the voltage before the short circuit.

So now the voltage across “Circuit Block 2” (referred as $V_{CB2}$) can be computed according to equation (10).

$$V_{CB2}=F_{shortcircuit}\times V_{CB1}$$

(10)

To this far, we have all the necessary ingredients to work out the power output form “Circuit Block 2”. The power output from “Circuit Block 2” is then computed as expressed in equation (11).

$$P_{{output}_{CB2}}=V_{CB2}\times I_{short\mathrm{}circuit\mathrm{}effect\mathrm{}current}$$

(11)

Figure 2. “Circuit Block 2”-Short Circuit Power Harnessing (“Circuit Block 2” illustrates the innovative approach to energy conservation and utilization).

Figure 2. “Circuit Block 2”-Short Circuit Power Harnessing (“Circuit Block 2” illustrates the innovative approach to energy conservation and utilization).

Remark 3:

The proposed circuit configuration (figure 2), while innovative in its application of diode characteristics to create a protective mechanism during short circuits, aligns seamlessly with established principles of semiconductor physics and diode behavior [57,58,59,60]. It adheres to the well-established properties of diodes in forward and reverse bias states, demonstrating a clear understanding of their depletion layer dynamics and the consequent influence on current flow.

4. Discussion and Implications

5. Conclusion

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