Battery connected to an infinite number of loads in parallel

[032050]

Homework Statement

Okay, so there is a battery with in internal resistance r and voltage of (V). The battery is hooked up to an infinite number (N) of lightbulbs each with resistance R in parallel. The question asks me to find the current going through the first lightbulb...My problem is when I am doing the question I'm out by a factor of N being the number of lights attached.

Homework Equations

V=IR
1/Rparallel=[1/R1+1/R2...]^-1
Rt=Rparallel+r

The Attempt at a Solution

Okay so i know that i can condense all the parallel loads to
Rparallel=(R/N)
then current through the first bulb would be I=V/(r+R/N)
except the solution has the I=1/N[V/(r+R/N)]

I have no idea where that 1/N factor came from, I've tried everything, almost i guess...
Thanks a lot in advance

 

[Doc Al]

Okay so i know that i can condense all the parallel loads to
Rparallel=(R/N)

OK.

then current through the first bulb would be I=V/(r+R/N)

That's the total current through all the bulbs.

 

[032050]

If I take 1/N of the total current and say that that is going through the first bulb is that not assuming that the current is evenly distributed to all the loads. whenever I have done questions where the current splits into two directions it hasn't been an even distribution of the current?

 

[Doc Al]

If I take 1/N of the total current and say that that is going through the first bulb is that not assuming that the current is evenly distributed to all the loads.

Yes.

whenever I have done questions where the current splits into two directions it hasn't been an even distribution of the current?

If each branch is identical--as is the case here--why shouldn't the current split evenly?

 

[032050]

Oh I never thought of that okay thanks a lot!