# Will current flow if Circuit contains a single cell?

I was thinking about this question and I can't figure it out....

If an electrical circuit contains just a single cell (internal resistance(r)=$0$) and conducting wires with $0$ resistance, then will current flow through the circuit? ...

''My thoughts:'' According to Ohm's Law...Voltage difference(V) $=IR=0$.. So..as potential difference is zero...charge will not flow?...

• If the resistance is zero you don't need a non-zero voltage to have a current. – nasu May 19 '17 at 15:50
• @nasu..but you need to supply energy to start the current – user35508 May 19 '17 at 15:53
• You are using ohms law! Seriously! ... + it is indeterminate form since current will tend to infinite – Utkarsh futous May 19 '17 at 16:05
• Magic. If you can have zero internal resistance and zero resistance resistors, then you can use the same trick to start the current. But on a serious note, you can have a superconducting ring and the current could be induced with an external magnetic field. – nasu May 19 '17 at 16:08
• Generally, our physical theories cannot provide predictions for physically impossible situations. That is the case here. – garyp May 19 '17 at 18:00

## 1 Answer

First, you conclusion doesn't follow. If the total resistance (internal plus external) is actually zero and you apply Ohm's law, the voltage across is zero for any finite current through.

But if the cell has zero internal resistance as you stipulate, the terminal voltage must be non-zero and so you arrive at a contradiction, e.g., 1.5V = 0V.

If instead one starts with the external resistance $R = 0$ and let the internal resistance go to zero $r \rightarrow 0$, one sees that the current goes to infinity $I \rightarrow \infty$.

But no physical cell can supply arbitrarily large current and so you conclude that no physical cell can have zero internal resistance, i.e., any physical cell has a maximum short-circuit current.

Further, any physical arrangement of a wire and cell will have inescapable inductance since a loop is formed through which magnetic flux can thread.

At the point that the total circuit resistance becomes insignificant compared to the circuit inductance, you more or less discard Ohm's law and look at the fact that the inductance and cell voltage limit the time rate of change of current.

Finally, there is also inescapable capacitance and radiation resistance that might need to be considered.