A, if the light is broken, the whole circuit is broken, the light bulb is not lit, and the voltmeter displays the numbers. This option is correct;

B, if the resistor R is short-circuited, the light bulb emits light; So it doesn't fit the meaning of the question. This option is wrong.

If the resistor R is open, the light bulb is open, so the light bulb is not lit; The voltmeter measures the power supply voltage, but these phenomena can also occur when the bulb is short-circuited. This option is wrong;

CD, if the light L is short-circuited, the light bulb will not light up; The voltmeter measures the voltage of the wire, so there is no indication. At the same time, if the resistor R is disconnected and the light bulb is disconnected, then the light bulb is not lit and the voltmeter has no indication, and the phenomenon is the same. So the CD option is too absolute, so both options are wrong;

So choose a.