\(b.\) Bulbs 1 and 2 get dimmer
\(c.\) Bulb 1 gets brighter and bulb 2 gets dimmer
\(d.\) Bulb 1 gets dimmer and bulb 2 gets brighter
\(e.\) Bulbs 1 and 2 stay the same
What has changed between these two states? We put in another resitor, so there was definitely a change in equivalent resistance.
We added another element in parallel with resistor 2. and we know that adding an element in parallel lowers resistance.
the total current through the whole resistor network is equal to the current through element 1, since element 1 is in series with the rest of the circuit.
The current in element 1 rises, since the total current rose.
Bulb 1 gets brighter
This eliminates answers B, D, and E
We found out in the previous section that element 1 has more current. This means, by Ohm's law, that it is also consuming more voltage.
If element 1 is consuming more voltage, then that means that the rest of the circuit (element 2 and the new element) must have a lower voltage drop than before, since the two must add up to the source in either case.
And resistor 2 is in a parallel configuration. The voltage across a parallel configuration is identical to the voltage across each of the elements. That voltage just dropped.
And with lower voltage comes lower current, and with lower current comes lower brightness.
Therefore, bulb 2 gets dimmer