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Show that the two expressions for inductance given by

$$L=\frac{N \Phi_{\mathrm{B}}}{I} \quad \text { and } \quad L=\frac{-\boldsymbol{\varepsilon}}{\Delta I / \Delta t}$$

have the same units.

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University of Michigan - Ann Arbor

Numerade Educator

Hope College

University of Winnipeg

for this question were asked to show that these two expressions for induction ce have the same units. So let's go ahead and work on the first expression. Never have turns times the magnetic foots divided by the current. Okay, well, the number of turns is unit Lis. The magnetic flux has units of Tesla times meters squared in the units of the current are and pierce. Okay, so we can go ahead and rearrange this and simplify it here. So Tesla unit is Newton's divided by cool ums times meters per second. So this is gonna be meters here. Then you also get it. You can move that seconds to the top. So that's a unit of a Tesla. This is still multiplied by meters squared. It's a bad what? We draw it divided by amperes. So simplifying this even even further. This squared cancels with that end. So we're left with Newton's time seconds times meters divided by cool homes times amperes. Okay, well, a Newton times a meter. Is it Jule? And a jewel. Per Coolum is a vault. So this is volts Time seconds praying Pierce. And the reason we converted toe volts is gonna come become apparent soon. So the second equation is the IMF, divided by the change in the current, divided by the change in time. So this becomes voltage because that's the current change in time goes on top that has units of seconds divided by changing, uh, current, which is units of amperes. So as you can see, this matches this, they have the same units.