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Well ,I know that current can flow through a zero resistance wire if potential difference across its ends is 0 because once electrons are set into motion by application of electric field for a moment in that 0 resistance wire , they keep on flowing . But ,I was thinking what will happen to the current if we apply potential difference across its ends ? According to OHM's law if V is finite and R->0 then I should approach to infinity .Does this really happens or ohm's law fail in this case ? If this is the case as per OHM's law then why don't we apply potential across a superconductor and then it could produce enough current for the world .

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    $\begingroup$ How do you propose to apply this potential difference? $\endgroup$
    – nasu
    Commented May 31, 2021 at 20:51

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The Ohm's Law is valid for a steady state condition. If we apply a voltage between the ends of any wire, the current is initially zero, and takes some (very small) time to reach the steady state $I = \frac{V}{R}$. While it is increasing, voltage is also proportional to the rate of growth, $$V = L \frac{dI}{dt} + RI$$ where $L$ is the inductance of the wire. The solution is:

$$I = \frac{V}{R}(1 + e^{\frac{-Rt}{L}})$$

When $R > > L$ the exponential term fades quickly, converging to the Ohm's Law.

When $R = 0$, the differential equation is simply: $$V = L \frac{dI}{dt}$$ with the solution:$$I = \frac{Vt}{L}$$

The current will grow linearly while the source can deliver a constant voltage.

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