[单选题]
Two identical lamps
cye8k0: 3qf19 q by()rsshstn ij1p)s9 p g4yhy:bhk* kt)/ph$L_1$ and $L_2$ are connected to a cell with no internal resistance as shown below. Resistors $R_1$ and $R_2$ are also identical. Switch $S$ controls part of the circuit.
Which of the following statements about the brightness of the lamp $L_2$ are correct?
I. If the resistance of $R_2$ increases, the brightness of $L_2$ increases.
II. If the resistance of $R_1$ increases, the brightness of $L_2$ decreases.
III. If switch $S$ is opened, the brightness of $L_2$ does not change.