# Does emf (electromotive force) exist between the points A and B in the image? If it exists what is the value?

The battery has no internal resistance and the wire doesn't have any resistance.The circuit is in ideal conditions.

I know that current won't flow in the circuit because,if it flows, the potential difference between A and B in the top circuit will differ from the potential difference between A and B in the bottom circuit. But I am not sure about the value of potential difference between A and B.

By Kirchhoff's Voltage Law (KVL), the voltage across nodes $A$ and $B$ is given by (assuming the circuit current $I$ circulates clockwise)

$$V_{AB} = V + V_{R1} = V - V_{R2}$$

I know that current won't flow in the circuit

That's correct (unless $R_1 = R_2 = 0$) and so you now have all that you need to answer your own question.

• Also if the resistors are absent, no current flows. – my2cts Jun 14 '18 at 18:49
• @my2cts, by absent do you mean removed (as in open the circuit there) or do you mean replaced with wires. If the former then yes, there is zero current. But if the latter, then the current $I$ is a free variable (no ideal circuit law constrains $I$ to be zero). – Hal Hollis Jun 14 '18 at 20:03
• By absent I mean zero resistance. There is no current whatever the resistance values, because both voltage sources combined produce zero output voltage. – my2cts Jun 14 '18 at 20:49
• @my2cts, this isn't true since the OP has specified that the batteries have zero internal resistance and the wires have zero resistance. For this ideal case, the current $I$ can take any value. You can simulate this if you like (I have). Replace the resistors with wires and add a series constant current source. Run a DC sweep of the current and find that for any value of current, the voltage across the current source is zero. That is, the current source does not supply or receive any power; no work is done by or on the current source. Thus, the current source can be replaced with a wire. – Hal Hollis Jun 14 '18 at 22:15

If you know that the current won't flow (which is correct, because the loop emf is zero), then you can conclude that the voltage drop across the resistors would be zero and, therefore, the voltage between $A$ and $B$ would be just $V$ or the voltage of the batteries.

It is tempting to think that, if there is a non-zero voltage between two points, $A$ and $B$ in this case, a current should flow between them, but there are many cases when it would not flow, for instance, when there is no conductor or, like in this case, the voltage is opposed by another, equal, voltage.