PHYSIC 難題22

I suppose the voltmeter is assumed to be ideal (i.e. of infinite resistance) and the two resistors are of 8 ohms each.
You want to know the voltmeter reading when (a) the switch K is open; and (b) the switch K is closed.

(a) When K is open, the circuit is incomplete (open circuit), as the voltmeter is of infinite resistance. There is no current flows through the circuit. The potential defference across the voltmeter equals to the emf of the battery, i.e. 10 volts.

(b) When K is closed, the voltmeter measures the potential difference across AB. But AB is of zero potential difference. Thus the voltmeter reading is 0 volt.

I cannot see the resistance clearly. Maybe assume two resistant is 8Ω.
when the switch is open.ed we can ignore the switch. the voltmeter's resistance is infinite, so there is no current throw the circuit. the voltage between the volmeter is equal to the battery(10V).

when the switch is closed. because the vlotmeter's resistance is infinite, so the current throwing voltmeter and resistance is zero. we can ignore it. so the voltmetre is zere V

I hope it can help you!!