How can voltage drop be zero if E-field isn't?

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greypilgrim
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Hi.
I learned that in an ideal conductor in a circuit, the voltage drop is zero. But how does this agree with the basic definition of voltage
$$U_{AB}=\int_A^B \vec{E}\cdot d\vec{s}\enspace ?$$
The electric field inside a conductor only vanishes in static conditions, but in an electric circuit, it makes up the driving force of the current and is obviously nonzero.
 
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