In the given figure end A is connected to positive terminal and B with negative terminal of a 10 volts battery. How exactly will the current flow?

Question

Further in my textbook it is stated that the ends of all three resistors are under the same potential difference. how is that possible?

Answer 1

A is at 10V and is connected by a (perfect 0-resistance, so no voltage drop across it) wire to 2, so 2 is at 10V. B is at 0V and is connected by a wire to 1, so 1 is at 0V. So the potential difference across the $6\Omega$ resistor is the difference between A and 1: 10V. The potential difference across the $15\Omega$ resistor is the difference between 2 and B: 10V. The potential difference across the $10\Omega$ resistor is the difference between 2 and 1: 10V. Now use Ohm's law to find the current through each resistor.