In the following circuit diagram, the power supply voltage U is constant, and the rated voltage of the small bulb is U0.

When the switch is turned to 1, the resistance and voltage at both ends of the bulb can be obtained, assuming that it is u1;

When the switch is turned to 2, the voltage at both ends of the bulb can be found, assuming U2;

Then the voltage across the resistor is u1-U2; If the resistance value is r, the current flowing is (u1-U2)/r;

So the power of the light bulb: p = U2 * (u1-U2)/r.