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Show that the units $1 \mathrm{A}^{2} \cdot \Omega=1 \mathrm{W},$ as implied by the equation $P=I^{2} R$

$[\mathrm{W}]=\left[\mathrm{A}^{2} \cdot \Omega\right]$

Physics 102 Electricity and Magnetism

Chapter 20

Electric Current, Resistance, and Ohm's Law

Current, Resistance, and Electromotive Force

Riza J.

November 26, 2020

University of Michigan - Ann Arbor

Simon Fraser University

Hope College

McMaster University

Lectures

11:53

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In this particular problem, we need to prove that 1 per square ohm is equal to 1 watt. We'Ll start with the step a here since we know that b is equal to i square multiplied by r. So therefore, the unit of power can be calculated. As i write it in brackets, so watts is equal to that is ampere square multiplied by ohms step b would be by using ohm's law is equal to current into resistance multiplication. So i write it as v is equal to y into r. So, oh here it will be in brackets, r is equal to v over. I now we need to substitute units. We get therefore ohm for r v, 4 voltage and amperes for current and we'll mention this as the equation 1 step. In this case, we need to rewrite the unit of power, as so p is equal to p r square. Oh, and this we will consider as equation 2 now in the next set from equation. 1 put the value of ohm into equation 2. So therefore, we'll write it as p is equal to v square and the ratio of v upon a so. Ultimately, it will be a multiplication of v and a so therefore, p is equal to v into a step. T would be let us substitute 1 coulomb over 1, second for 1 ampere and 1 joules per 1 coulomb for 1 volt. Now solving this further we get since power is equal to ion to therefore p is equal to, for i will substitute 1 coulomb to 1. Second, multiplied by 1, joules per 1 comes here: 1 grom gets canceled and 1 joule per 1. Second, is the ratio that we get and which is equal to 1 watso? Ultimately, hence it is verified. It is verified that unit amperes ohm is equal to 1 at.

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