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Physics
Classical Physics
Electromagnetism
Deriving expression for resistance in terms of current density
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[QUOTE="alan123hk, post: 6830095, member: 638884"] A very useful equation is shown here [CENTER][ATTACH type="full" width="650px" alt="Circuit-33.jpg"]318527[/ATTACH][/CENTER] $$ V_1-V_2=IR_{12}-\varepsilon _{12}~~~~~\Rightarrow ~~~~~V_1-V_2=IR_{12}-\int_1^2~dl\cdot~E^{'} $$ That is to say, the voltage difference in a circuit with EMF is not equal to IR, but equal to IR minus EMF. This is actually an equation very familiar and commonly used by electrical and electronics engineers when conducting circuit analysis. It is also worth noting that $$IR_{12}=(V_1-V_2)+\varepsilon _{12}=\int_1^2~dl\cdot~(E+E^{'}),~~~~\text{so}~~R=\frac {1}{I} \int_1^2~dl\cdot~(E+E^{'}) $$ Everything is in perfect harmony, without contradictions. :smile: [/QUOTE]
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Forums
Physics
Classical Physics
Electromagnetism
Deriving expression for resistance in terms of current density
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