Comparing the brightness of each bulb in a circuit

[omnislash]

Homework Statement

Four identical light bulbs are connected to a battery as shown in the diagram. Switch S is originally closed. If switch S is opened, what happens to the brightness of each bulb?

Homework Equations

V=IR

The Attempt at a Solution

- By opening the switch, no more current flows through bulb 2
- Therefore, the equivalent resistance of the bulbs in that branch increase
- Current produced by battery decreases, which means the current entering the junction is lower than before

This is where the problem beings:
- I said that bulb 1 would be dimmer since it has less current flowing through it, but it turned out that the brightness never changed
- I said bulb 3 receives less current and has greater equivalent resistance, so the brightness never changed. I was wrong
- I am clueless on bulb 4

Can somebody help me out?

 

[haruspex]

Circuit produced by battery decreases,

They want you to assume an ideal battery, i.e. no internal resistance, so the voltage there does not change.

bulb 3 receives less current

Why?

 

[omnislash]

They want you to assume an ideal battery, i.e. no internal resistance, so the voltage there does not change.

Why?

Total resistance of the circuit increases, the voltage stays constant, so the current flowing through battery decreases. This should mean that the current entering the junction between the switch and bulb 3 decreases

 

[haruspex]

Total resistance of the circuit increases, the voltage stays constant, so the current flowing through battery decreases. This should mean that the current entering the junction between the switch and bulb 3 decreases

Right, but we know that no current is going to bulb 2 now, so how does that tell you whether the current through bulb three has increased or decreased?

 

[neilparker62]

An approach you could try is assign arbitrary numeric values to the emf of the battery and resistance of bulbs: then solve the circuit for when the switch is closed and separately when it is open. Eg: V(battery)=12 V and R=4ohms.

 

[omnislash]

Right, but we know that no current is going to bulb 2 now, so how does that tell you whether the current through bulb three has increased or decreased?

Since a bulb is eliminated from parallel (resistance), this tells us that the equivalent resistance on bulb 3 is greater. So, less current through bulb 3...

 

[haruspex]

Since a bulb is eliminated from parallel (resistance), this tells us that the equivalent resistance on bulb 3 is greater. So, less current through bulb 3...

No, it tells you the equivalent resistance between the terminals of bulb 3 has increased, so the total current flow between those points has decreased; but that is hardly surprising since there is now no current flowing through bulb 2, so it does not tell you whether the current through bulb 3 has increased or decreased.
The resistance of bulb 3 has not changed, so think about the voltage across bulb 3. How has that changed?