Electrical Energy & Formula | How to Calculate Electrical Power – Video & Lesson Transcript | Study.com

Power in an Electric Circuit

Power is the amount of energy provided by an electrical circuit each second. For example, an old-fashioned 60-watt light bulb provides exactly 60 joules of energy (in the forms of both light and heat) to the room each second it is turned on. A modern LED lightbulb, on the other hand, might only use 10 watts of energy, while providing the same amount of light. This means that circuit is using 10 joules of energy per second while saving 50 joules of energy each second. Modern lightbulbs are able to accomplish this because they generate only light and no heat.

Hydroelectric dams produce huge quantities of both power and energy.

The same units are used to measure the productivity of modern power plants. A large hydroelectric dam, like the Hoover Dam, is rated at 2,080 megawatts. This means, when operating at full capacity, it generates 2,080 million watts of power. This equates to 2,080,000,000 joules of energy each second. This is enough electricity to power about 1.3 million households.

How to Calculate Power in a Circuit

Calculating the amount of power generated by an electrical circuit requires one simple formula, but it also requires an understanding of a few different concepts. First, one must understand voltage. Voltage is measured in volts and is usually defined as the difference in electrical potential energy between two points in a circuit. But it might be more easily understood as a form of electron pressure. When electrons are packed tightly together, they repel each other due to their negative electrical charge. The more electrons are packed together (in a battery, for instance), the more they want to spread out and move to an area with more space. Thus, the more electrons are packed together, the greater the pressure, and the higher the voltage.

The second concept one must understand is electrical current. Current is measured in amps, and it is usually defined as a measure of the number of flowing electrons per unit time. The more electrons are flowing, the higher the amount of current. Thus, the current is directly affected by variables like the thickness of a wire and also variables like voltage. The higher the voltage, the faster the electrons will flow through the circuit.

The third concept one must understand is resistance. Resistance is measured in ohms and is usually defined as the degree of opposition to the flow of electrons. A thin wire, for example, would have more resistance than a thick wire. And a material like rubber would have much more resistance than a material like copper.

Flashlights are a simple circuit containing a battery and a lightbulb.

In 1827, German scientist Georg Ohm published a book that put all of the above together. It included a relationship now known as Ohm’s Law. The law says that the amount of current flowing through a circuit is proportional to the amount of voltage in the circuit and inversely proportional to the amount of resistance in the circuit. More voltage will increase the current. More resistance will decrease the current. And thus, the three variables can be combined into the following formula.

{eq}I = V/R {/eq}

I stands for current, measured in amps. V stands for voltage, measured in volts. And R stands for resistance, measured in ohms. The formula can easily be rearranged into another very common form: V = IR.

All of this brings us back to power. Power depends upon both the electron pressure (voltage) and the number of electrons (current). The amount of power a circuit produced can be calculated using the following formula.

{eq}P=IV {/eq}

P stands for power, measured in watts. I stands for current, measured in amps. And V stands for voltage, measured in volts. Using this formula, calculating the amount of power generated by a circuit is a matter of using both of the above formulas. Take, for example, a simple flashlight powered by a 9-volt battery and using a small lightbulb with 10 ohms of resistance.

I=V/R

I=9/10

I=0.9 amps

P=IV

P=0.9*9

P=8.1 watts

First, the amount of current flowing through the circuit must be calculated using Ohm’s Law. Second, the amount of power can be calculated by multiplying current times voltage. The process yields an answer of 8.1 watts, which makes sense, given that a simple flashlight is less powerful than a typical household light bulb.

Electrical Energy Formula

Calculating the amount of total energy produced by a circuit is different than calculating power. Power can be thought of as energy per unit time. Energy is simply energy, and it depends very much on the amount of time. Running a flashlight for an hour, for example, uses much more energy than running a flashlight for a minute.

In order to calculate the total energy flowing through a circuit, one must know the power it generated (in watts), as well as the amount of time energy, was flowing (in seconds). Put together, the formula for calculating energy in a circuit is as follows.

{eq}E=PT {/eq}

E stands for energy, measured in joules. P stands for power, measured in watts. And T stands for time, measure in seconds. Using this formula, we can easily calculate the amount of energy used by our flashlight if we run the flashlight for a full hour. First, we will need to recall that it is an 8.1-watt flashlight. Second, we will need to know that the amount of seconds in an hour (60 seconds times 60 minutes) is 3,600. Then, we can use our formula.

E=PT

E=8.1*3,600

E=29,160 joules

Altogether, we have determined that a small flashlight does not use very much energy. The number 29,160 might sound like a lot, but joules are a very small unit. This number equates to roughly 7 Calories, roughly the amount of food energy contained by just two M&Ms.

Lesson Summary

An electrical circuit is a closed loop that allows electrons to flow from a voltage source, through any number of elements, and then toward an area of lower voltage. The amount of energy carried by moving electrons depends upon both how tightly they are packed (voltage) and the amount of moving electrons (current). The total energy is measured in joules, while a circuit’s power is measured in watts (joules per second).

Calculating power in an electrical circuit requires knowledge of a few different concepts. First is voltage (V), which can be thought of as electron pressure. The second is current (I), which can be thought of as the number of flowing electrons. The third is resistance (R), which is opposition to electron flow. Put together, one can use Ohm’s Law (I=V/R) to calculate any of the three above variables. And using the formula P=IV, one can calculate the amount of power (P) flowing through a circuit. But total energy (E) depends upon power and also time. To calculate the amount of energy used by a circuit, one must use the formula E=PT.