Could this bulb resistance problem be modified ?

[Jahnavi]

Homework Statement

Homework Equations

The Attempt at a Solution

The original question given above has been correctly answered by me .The correct option is 2) .

Thinking more about this problem made me wonder if there could be a combination of L1,L2,L3(different from that given in the question) for which , if L3 fuses , L2 gets dimmer .The geometry of the problem is kept same .

I tried few different combinations , but ended up with the same result i.e L2 glows brighter when L3 fuses .

I have no problem with L1 getting dimmer when L3 fuses . Since the net resistance of the circuit increases when L3 fuses , L1 has to get dimmer for any combination of L1,L2,L3 .

But what about L2 ? Does it glow brighter for every combination of L1,L2,L3 (keeping the geometry same )?

Could anyone give a combination of resistances for which L2 gets dimmer when L3 fuses out ?

 

[mfb]

It always gets brighter. L1 always gets dimmer, which means the voltage at L1 drops, this means the voltage at L2 increases.

 

[Jahnavi]

It always gets brighter. L1 always gets dimmer, which means the voltage at L1 drops, this means the voltage at L2 increases.

Your reasoning is very nice

Thanks !

 

[CWatters]

Ok different problem but...

If you remove L3 so you just have L1 and L2 and then vary the resistance of L2 you will find that there is a value for L2 that maximises the power dissipated in L2.

For example if L2 had a very low resistance then there would be no voltage across L2 so no power dissipated in L2. If L2 was very large the current would be very low so again no power would be dissipated in L2.

Try calculating the value required to maximise the power dissipation in L2.