Why current flows in a resistor connected with a battery although there is zero potential difference between one end of the battery and one end of the resistor?

Hint: Firstly, understand that terminals used to measure the potential difference across the resistor are wrong. If you want to see whether there is potential difference across a given resistor or any element, you have to measure it across it. Maybe, you could recall the ohm’s law to give a better justification.

Complete answer:
In the given question, we are given a simple electric circuit in which a resistor is connected with a battery. Then, we are asked why there is a flow of current in the resistor when there is zero potential difference between one end of the battery and one end of the resistor.
For a student who is thorough with the concepts of current electricity may find this question quite meaningless.

As per the question, the potential difference when measured between the points A and C (or B and D) is found to be zero. But that is not how we measure potential difference for an element (here, resistor).
The battery here provides a voltage of V volts. So when we keep a voltmeter across A and B we find the reading to be V volts. Similarly, when we measure the potential difference for the resistor we have to measure it across its two terminals that are C and D and we find it also to be V volts. And wherever there is a potential difference, the current will surely flow.

Note:
We know ohm’s law which is given by,
$I=\dfrac{V}{R}$
Where, V is the potential difference (voltage), I is the current and R is the resistance. So for zero potential difference there will be no flow of current. But when the resistance is zero, there will be infinite current flowing through the circuit. So if there is current flowing through a circuit there surely is a potential difference.