Physics Lesson 15.6.1 - Mechanical Power Recap. The Meaning of Electric Power

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Welcome to our Physics lesson on Mechanical Power Recap. The Meaning of Electric Power, this is the first lesson of our suite of physics lessons covering the topic of Electric Power and Efficiency, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Mechanical Power Recap. The Meaning of Electric Power

In tutorial 5.5 "Power and Efficiency" we have discussed the concept of mechanical power which is the work done by an object or system in the unit of time. Mathematically,

P = W/t

Given that work is the force F needed to move an object by Δx metres, we obtain for mechanical power

P = F ∙ ∆x/t
= F ∙ ∆x/t
= F ∙ v

where v is the velocity of the moving object.

However, work does not imply only being able to move an object by some linear distance. It also means delivering energy in the form of heat. This occurs in thermal systems where the power of such systems is evaluated by their ability to deliver heat energy in a given time.

The unit of power is [J/s] or watt [W]. However, when expressed in terms of fundamental SI units, the unit of power becomes

[W] = [J/s] = [N ∙ m/s] = [kg ∙ m/s² ∙ m/s] = [kg ∙ m²/s³ ]

Likewise, electric power is the work done by an electric source during a given time. Given that the strength of an electric source is determined by its electromotive force, we must express the power delivered by such a source in terms of the work done by the source to make the charges move through a circuit. Obviously, this work does not depend only on the strength of the source but also on the length of the path along which the electric charges will move to do the required work. In other words, the role of displacement in the mechanical power here is played by the length of the circuit (the length of conducting wire), while the force necessary to move the charges is provided by the electric source, which has a certain electromotive force.

We have explained earlier that the electromotive force of an electric source represents the work done by this source to make the charges flow through the circuit, i.e.

emf = W/Q
= F ∙ L/Q

where L is the length of the conducting wire and Q is the charge. Therefore, the force provided by the source is

F = emf ∙ Q/L

Henceforth, we will denote the electromotive force by ε instead of emf. In this way, the formula of electric force provided by the source becomes

F = ε ∙ Q/L

Since the electric power is similar in concept to mechanical power, i.e. it represents the work done by the electric source in the unit of time, we obtain (after substituting Δx in the mechanical power with the length L of conductor):

P = F ∙ L/t
= ε ∙ Q/L ∙ L/t
= ε ∙ Q/t

From the definition of electric current I, we have

I= Q/t ⇒ Q = I ∙ t

Thus, we obtain after making these substitutions in the previous formula:

P = ε ∙ I ∙ t/t

P = ε ∙ I

Hence, the formula of electric power requires knowing only the electromotive force of the source and the electric current flowing through the circuit.

Example 1

What is the power of the electric source shown in the figure?

Physics Tutorials: This image provides visual information for the physics tutorial Electric Power and Efficiency

Solution 2

First, we find the equivalent resistance of the circuit. The resistance of the parallel branch is

1/R^p = 1/R₁ + 1/R₂
= 1/12 + 1/20
= 5/60 + 3/60
= 8/60

Thus,

R^p = 60/8 Ω
= 7.5 Ω

The equivalent resistance of the circuit therefore is

R_eq = R^p + R₃
= 7.5Ω + 3Ω
= 10.5Ω

The current flowing in the circuit is

I= ε/R_eq
= 21 V/10.5 Ω
= 2 A

From here, we can calculate the power of the circuit:

P = I ∙ ε
= 2A ∙ 21 V
= 42 W

You have reached the end of Physics lesson 15.6.1 Mechanical Power Recap. The Meaning of Electric Power. There are 4 lessons in this physics tutorial covering Electric Power and Efficiency, you can access all the lessons from this tutorial below.

More Electric Power and Efficiency Lessons and Learning Resources

Electrodynamics Learning Material
Tutorial ID	Physics Tutorial Title	Revision Notes	Revision Questions
15.6	Electric Power and Efficiency
Lesson ID	Physics Lesson Title	Lesson	Video Lesson
15.6.1	Mechanical Power Recap. The Meaning of Electric Power
15.6.2	Input and Output Electric Power. Joule's Law
15.6.3	Joule or kW-h?
15.6.4	Other Forms of Writing the Formula of Electric Power

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