How Many Bulbs Are Connected to Match Internal Resistance Voltage Drop?

[Biosyn]

Homework Statement

A battery has an internal resistance of 0.50 ohm. A number of identical light bulbs, each with a resistance of 15 ohm, are connected in parallel across the battery terminals. The terminal voltage of the batter is observed to be one-half the EMF of the battery. How many bulbs are connected?

Homework Equations

V = V_emf - IR

The Attempt at a Solution

n = number of light bulbs

1/(R_b) = (1/15)n
R_b = 15/n

I'm not sure what to do at this point..

V = (1/2)V_emf

 

[Villyer]

What can be said about the current in the battery and the current in the circuit?

 

[Biosyn]

What can be said about the current in the battery and the current in the circuit?

The current is the same?

My thoughts:
Is the voltage split in half? Because half of the voltage goes through the circuit and the other half is going across the internal resistance?
So...are the internal resistance and the resistance of the bulbs equal?

 

[Villyer]

The current is the same?

My thoughts:
Is the voltage split in half? Because half of the voltage goes through the circuit and the other half is going across the internal resistance?
So...are the internal resistance and the resistance of the bulbs equal?

Exactly.

Because the voltage is split in half (therefore equal) as you say, and the currents are the same, by the equation V=IR the resistances have to be the same.

 

[Biosyn]

Exactly.

Because the voltage is split in half (therefore equal) as you say, and the currents are the same, by the equation V=IR the resistances have to be the same.

. so that must mean:

r = R

15/n = 0.5

n = 30

Thanks for helping!

 

[gneill]

The current is the same?

My thoughts:
Is the voltage split in half? Because half of the voltage goes through the circuit and the other half is going across the internal resistance?
So...are the internal resistance and the resistance of the bulbs equal?

To be more precise, half the voltage is dropped across the internal resistance and the other half is dropped across the external resistance. Current goes though, potential drops across components.