Electric Power Formula: Derivation, Power Energy Formula

Electric Power measures the rate of electrical energy that is transferred by an electric circuit per unit of time. It is commonly produced by electric generators or supplied by electric batteries. Power is denoted by ‘P’ and its SI unit is Watt. The electric power can be calculated by the electric power formula P = VI.

Key Terms:- Electric Power, Ohm’s Law, Electrical energy, Watt, Voltage, Charge, Resistance.

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Electric Power Formula

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The formula for electrical power has been derived from Ohm’s Law. It connects time, voltage, and charge. The formula for electric power is:

P = IV

By Ohm’s Law, it can also be written as:

P = I²R

Or

P = V²/R

Where,

• P = Electric Power
• I = Electric current
• R = Resistance
• V = Voltage or Potential difference

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Power Energy Formula

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Power is the rate of consumption of energy. The electric circuit element is positive and negative periodically over some interval of time, depending upon the sign of the power integral. If the power is constant over the time interval, power consumption can be expressed as:

E = Pt

P = \(E \over t\)

Where,

• E = Energy Produced
• P =  Power Consumption
• T = Time period

Electric Power

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Derivation of Electric Power

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Power is the rate of doing work and similar is the electric power that corresponds to the rate of transfer of electric energy. Electric energy is derived from the kinetic energy of charged particles or potential energy.

Derivation of Electric Power

• Electrolytic battery has two terminals namely an anode and cathode, the positive and negative terminal.
• The potential difference which is developed across two terminals due to the flow of electrons is called emf (electromotive force) or voltage in simple words.
• Suppose an electrolytic battery with two terminals A and B has V1 and V2 voltage at terminals A and B respectively.
• The potential difference between both terminals is: V = abs (V₁-V₂)

As this is the arithmetic difference between voltages, it is always the positive quantity greater than zero.

Derivation of Electric Power

The electric current is the flow of electrons or the electric charges. Electric current is nothing but the rate of flow of electrical charges in a particular cross-sectional area. The kinetic energy of the particle which is conserved is stored in the form of potential energy. Let the potential energy of charge ‘q's at terminal A be qV₁ and the potential energy of charge ‘q’ at terminal B will be qV₂. Thus, is:

Total change in energy of the system

ΔU = final potential energy - initial potential energy

ΔU = Δq (V₂ – V₁)

ΔU = -IΔt V ( since, I = Δq/Δt)

If the total kinetic energy of the system is taken into account, then it will change if charges inside any conductor move without collision. This is basically to conserve the total energy of the system. By the law of conservation of energy, we can say:

• U = Kinetic Energy
• Kinetic Energy = -IVΔt > 0

Thus, when charges move freely across any conductor in an electric field, gradual energy in Kinetic Energy is observed.

When there is a collision in the charges, the total energy gained is shared among all the atoms. This gained energy increases the vibration of atoms within the conductor, and this heats the conductor. Hence, in this process, some energy is dissipated from the conductor in the form of heat.

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Things to Remember

• Electric power is the rate at which electrical energy is transferred through an electric circuit.
• It is denoted by P.
• The SI unit of power is Watt.
• The formulas for Power can be defined as: P = IV Or P = I²R Or P = V²/R
• One watt of power is said to be consumed if one joule of electric energy flows in one second time.
• The Commercial unit for power is Kwh.
• The electrical power conversion is 1 kwh = 36 x 105 Ws or Joules

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