Electric Power Formula

Physics is all about learning the mechanics of life. Work, energy, and power are the most important physical aspects that are widely used in the physical world. Physics involves many interesting concepts such as kinematics, one-dimensional motion, and many more and these are categorised under classical physics. Just like classical physics, there are various branches of physics depending upon the subject of discussion. Electrodynamics or electrical circuit theory is the study of electrical connections used in the day to day activities. Electric power is the most commonly used term in circuit theory. 

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The electric power formula deals with the rate of work. We know that power is the rate of doing work, similarly electric power is a very important thing that enables us to observe the rate at which electrical energy transfers from an electric circuit, i.e., rate of transfer of electrical energy. In this article, we will learn about the electric power formula, electrical energy formula, and the formula of power consumption with solved numerical.

Electrical Energy Formula

The electrical power formula is analogous to the mechanical power formula, we notice that electric power is the rate at which work is being done or in other words, electrical power is the rate at which electrical energy is transferred. The electrical power is measured in watts. Now, electrical energy is the energy derived from electric potential energy or kinetic energy of the charged particles. Electrical energy is a very important concept in physics, yet it is frequently misunderstood because of its definition. Then what exactly is electrical energy, what is the electrical energy formula and what are important steps and the rules that will be applied when it is used in calculations? 

Let us have a look at the electrical energy formula. We know that an electrolytic battery will have two terminals, one is positive and the other is negative, familiarly known as the anode and cathode of the battery. The potential difference developed between the two terminals is known as the voltage or emf.  Mathematically, let us assume that the two terminals of the battery are A and B, let V₁ and V₂ be the potentials at terminal A and B respectively. 

The potential difference (or the voltage) across terminal A and B is given by the following equation:

⇒ V = V₁-V₂ = -(V₂-V₁)…….(1)

and this must be a positive quantity i.e., must be greater than zero.

Now, we know that electric current is the flow of electrons or in other words flow of electrical charges, then we can define electrical current as the rate of conduction of electrical charges or the rate of flow of electrical charges in a given cross-sectional area. The kinetic energy of these charges will be conserved and hence the total electrical energy will be stored in the form of potential energy. Then the potential energy of the charge Q at terminal A will be equal to QV₁, similarly, the potential energy of the charge Q at terminal B will be Q V₂. Thus the total change in potential energy of the system is given by:

⇒ΔU=final potential energy - initial potential energy

⇒ΔU=ΔQ (V₂-V₁)

⇒ΔU = -I Δt V ( because I = \[\frac{ΔQ}{Δt}\]).......(2)

If we consider the total kinetic energy of the system into account, it would also change if the charges inside the conductor moved without collision. This is to maintain the total energy of the system unchanged. Thus, according to the law of conservation of total energy, we have:

⇒ Kinetic Energy = U

Or

⇒ Kinetic Energy = -I V Δt >0

Thus, in the external or internal electric field, if the charges move freely across the conductor, there would be a gradual increase in the kinetic energy as they move without any constraints.

When the charges undergo collision, the total energy gained by them is shared between the atoms. Consequently, the vibration of the atoms within the conductor will be increasing which in turn result in the heating up of the conductor. Thus, some amount of the total energy is dissipated in the form of heat in an actual conductor.

The electrical energy is measured in terms of the joule or watt-second. Electrical energy is said to be of one joule when one ampere of current flows through the given electrical circuit for a second when the potential difference of one volt is applied across it. 

The kilowatt-hour (kWh) is the commercial unit of electrical energy, which is also known as the Board of Trade unit (B.O.T). And usually, one kwh is called one unit.

1 kwh = 1000 x 60 x  60  watt – second

1 kwh = 36 x  10⁵ Ws or Joules

This equation is known as the electrical energy unit conversion formula or electrical unit calculation formula.

Formula of Power Consumption

We know that, according to the definition of the electrical power formula, it is the rate of transfer of electrical energy by an electrical circuit per unit of time. Here the total electrical energy can be either kinetic energy or potential energy. In most cases, only potential energy is considered, which is the energy stored in the system due to the relative positions of charged particles or electric fields. Now, how do we calculate the electric power? What is the formula of power consumption to be followed while solving the problems? 

The electrical power formula is given by:

⇒ P= VI

The electrical power formula is written by using ohms formulas and it is also known as the power voltage current formula and  is given by:

⇒ P = I²R=\[\frac{V^{2}}{R}\]

Now,  we should note that an electrical circuit element having a power profile that is both positive and negative over some period of time interval could consume or produce energy according to the sign of the integral of power. If the power is constant over the time interval then the energy or the formula of power consumption can be expressed simply as:

⇒ E = P t

The above expression is known as the formula of power consumption or electrical power equation.

Example

1. If the Current and Voltage of an Electric Circuit are Given as? 3 Amp and 10 Volts Respectively. Calculate the Electrical Power of the Circuit?

Solution:

Given,

The total current flowing in the circuit = I =3 amp

The potential difference measured across the circuit=V=10 volts

We are asked to determine the electric power, we know that the electric power formula is given by ohms formulas:

⇒ P = V x I

Where,

V-The applied voltage

I-The current flowing in the circuit

Substituting the required data or values in the above equation, we get:

⇒P =10 x 3 = 30 watts

Therefore, the total electrical power of the circuit is 30 watts.