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

$[\mathrm{W}]=\left[\frac{\mathrm{V}^{2}}{\Omega}\right]$

Physics 102 Electricity and Magnetism

Chapter 20

Electric Current, Resistance, and Ohm's Law

Current, Resistance, and Electromotive Force

Noelyn A.

February 16, 2021

Show that the units 1 A2 ? = 1 W, as implied by the equation P = I2R.

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Washington

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So, uh, for this problem, we want Thio testify that to the unit votes squid over home is equivalent to is equivalent to what's so, uh, to prove this. Ah, consistence consistency. We need to utilize a very simple circuit. So suppose we have a resisting here and we have a power here. So this is our This is V and ah, clearly the current just utilized homes law. The current in the circuit is ah I equal v over r, right and ah, the voltage across the resistor is the same as the voltage off the power. So according to the definition of the power on the register, we have p equal v times I write and I hear we have this expression. So I plucked this expression to design. So this becomes me times meaty but by our So this becomes a V squared of our right. So we also know that the unit for power is waltz and the unit on the right hand side is simply the votes squared over over over alms. So we just Webster on the consistency of this two units. What? It's ah, Quick is equivalent to this. Ah both squared over over alms

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