### Table of Contents

- Definition
- Formula
- Example using voltage and charge
- Example using power and time
- Example of heating element
- Calculator
- References

### Definition

**Electric energy** is another form of energy which is generated due to the flow of electric charge through a circuit. Any electric circuit which has voltage and current for a certain amount of time has electric energy.

The amount of electric energy a circuit has depends on the level of voltage or electrical current. The higher the voltage or current in a circuit, the higher its electric energy. Electric energy is also defined as the work required to move electric charge through a circuit in a particular amount of time.

As any other form of energy, electric energy can be **generated** using generators, dynamos or photovoltaic cells or **stored** in batteries, capacitors or magnetic fields.

### Formula

Electric energy can be calculated in two ways [1]:

- using electric charge and voltage
- using electric power and time

Electric energy is the product of voltage and electric charge.

_{e}= U · Q

where:

- E
_{e}[J] – electric energy, measured in joules [J] - U [V] – electric voltage, measured in volts [V]
- Q [C] – electric charge, measured in coulombs [C]

Electric charge is the product between electric current and time.

where:

- I [A] – electric current, measured in amperes [A]
- t [s] – time, measured in seconds [s]

Replacing equation (2) in (1) gives the formula of electric energy as:

_{e}= U · I · t

We know that electric power is the product between voltage and current:

_{e}= U · I

where:

- P
_{e}[W] – electric power, measured in watts [W]

If we replace equation (4) in (3), we can see that electric energy is the product electric power and time.

_{e}= P

_{e}· t

From Ohm’s law we know that voltage is the product between current and electric resistance.

where:

- R [Ω] – electric resistance, measured in watts [Ω]

From (6) we can derive the formula of electric current as:

Replacing equations (6) in (4), gives the formula for electric power as:

_{e}= R · I

^{2}

Replacing equations (7) in (8), gives the formula for electric power as:

_{e}= U

^{2}/ R

Replacing equations (8) and (9) in (5), gives the formulas for electric energy as:

_{e}= R · I

^{2}· t

_{e}= (U

^{2}/ R) · t

A summary of formulas to calculate electric energy is:

_{e}= U · Q

E

_{e}= P

_{e}· t

E

_{e}= U · I · t

E

_{e}= R · I

^{2}· t

E

_{e}= (U

^{2}/ R) · t

The most common units of measurement for **electric energy** are: joule [J] or Watt-hour [Wh] or kilowatt-hour [kWh].

### Example using voltage and charge

Calculate the electric energy generated for a charge of 150 coulombs to be moved across an electric circuit with a voltage drop of 12000 millivolts.

**Step 1**. Convert the voltage from [mV] to [V] by dividing the [mV] to 1000:

**Step 2**. Calculate the electric energy E_{e} [J] generated:

_{e}= U · Q = 12 · 150 = 1800 J

### Example using power and time

Calculate the electric energy consumed by an electric device with a rated power of 120 watts if it operates continuously for 2 hours.

**Step 1**. Convert the time from [h] to [s] by multiplying the [h] with 3600:

**Step 2**. Calculate the electric energy E_{e} [J] consumed by the electric device:

_{c}= P · t = 120 · 7200 = 864000 J

### Example of heating element

An electric dryer operates at 120 volts. It contains an heating element with the electric resistance of 10 ohms. Calculate what is the energy consumption in kilowatts hour [kWh] of the heating element for 0.5 hours of usage.

**Step 1**. Convert the time from [h] to [s] by multiplying the [h] with 3600:

**Step 2**. Calculate the electric power P_{e} [W] of the heating element:

_{e}= U

^{2}/ R = 1202 / 10 = 1440 W

**Step 3**. Calculate the electric energy E_{e} [J] of the heating element:

_{e}= P

_{e}· t = 1440 · 1800 = 2592000 J

**Step 4**. Convert the electric energy E_{e} from [J] to [kWh], by dividing the [J] to 3600000:

_{e}= 2592000 / 3600000 = 0.72 kWh

### Calculator

The electric energy calculator allows you to calculate the electric energy of a circuit. You need to enter at least two electrical parameters and the time of operation. You can enter one of this options:

- voltage, resistance and time
- voltage, current and time
- current, resistance and time
- power and time

Leave blank the other parameters

The default unit of measurement for energy is **Joule**. If you want the result displayed in another unit, use the drop down list to choose and click the CALCULATE button again.

### References

[1] David Halliday, Robert Resnick, Jearl Walker, Fundamentals of Physics, 7th edition, John Wiley & Sons, 2004.

[2] Benjamin Crowell, Light and Matter – Physics, 2007.

[3] Raymond A. Serway and John W. Jr. Jewett, Physics for Scientists and Engineers, 6th edition, Brooks/Cole Publishing Co.,2004

[4] Jiansong Li, Jiyun Zhao, and Xiaochun Zhang, A Novel Energy Recovery System Integrating Flywheel and Flow Regeneration for a Hydraulic Excavator Boom System, Energies 2020.

[5] Leo H. Holthuijsen, Waves in oceanic and coastal waters, Cambridge University Press, 2007.

[6] Kira Grogg, Harvesting the Wind: The Physics of Wind Turbines, Carleton College, 2005.