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jafisika

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In our textbook (Fundamentals of physics, John Wiley and sons, 2008) many formulas are derived by treating a differential fraction (like dq/dt) as an ordinary fraction -see example below. Can this differential fraction in all cases be treated as a normal fraction. If not in all cases, when can it be treated as such?

Example of deriving a formula from Fundamentals of physics (2008): Note: E is the emf of an ideal battery and i is the current through the battery.

dW=Edq=Eidt

From conservation of energy:

Eidt= (i^2)Rdt, which gives

E=iR and thus i=E/R