Answer
a. Nothing happens.
b. The bulbs become dimmer.
Work Step by Step
a. When the switch is closed, the resistor is added in parallel to the branches already there. This lowers the equivalent resistance of the circuit, so the current that the battery supplies will increase.
We are told that this is an ideal battery with zero internal resistance, so the extra current will not affect the terminal voltage (page 833). The branches containing the bulbs still have the same voltage drop across them, so the bulbs do not change in brightness.
b. When the switch is closed, the resistor is added in parallel to the branches already there. This lowers the equivalent resistance of the circuit, so the current that the battery supplies will increase.
We are told that this is a real battery with nonnegligible internal resistance, so the extra current will lower the terminal voltage (page 833). The branches containing the bulbs now have a lower voltage drop across them, so the bulbs decrease in brightness.