Physics Lesson 15.6.4 - Other Forms of Writing the Formula of Electric Power

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Welcome to our Physics lesson on Other Forms of Writing the Formula of Electric Power, this is the fourth 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.

Other Forms of Writing the Formula of Electric Power

From Ohm's Law, we know that

∆V = I ∙ R

for a certain appliance and

ε = I ∙ R_tot

for the whole circuit. Substituting these two formulae in the equations of output and input power, we obtain

P_output = I ∙ ∆V
= I ∙ I ∙ R
= I² ∙ R

and

P_intput = I ∙ ε
= I ∙ I ∙ R_tot
= I² ∙ R_tot

These formulae are used when current and resistances are given but not the potential difference of electromotive force.

On the other hand, when potential difference (or emf) and resistance (but not the current) are given, we write

P_output = I ∙ ∆V
= ∆V/R ∙ ∆V
= ∆V²/R

for a certain appliance and

P_intput = I ∙ ε
= ε/R ∙ ε
= ε²/R

for the whole circuit.

Multiplying the above expressions by the time t, we obtain the work done (the useful energy consumed) by the appliance and the total energy delivered by the source in terms of resistance R:

W = I² ∙ R ∙ t
W = ∆V²/R ∙ t
E_tot = I² ∙ R_tot ∙ t

and

E_tot = ∆V²/R_tot ∙ t

Example 4

An electric heater has 1200 W of output power. If the heater operates at 240 V, what is the resistance of heater?

Solution 4

In this exercise, the current and resistance are not given, so we can use the formula

P_output = ∆V²/R

to calculate the resistance, where ΔV = 240 V and P_output = 1200 W.

Hence, we have

R = ∆V²/P_output
= (240 V)²/1200 W
= 57600 V²/1200 W
= 48 Ω

You have reached the end of Physics lesson 15.6.4 Other Forms of Writing the Formula 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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