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

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Homework Help Overview

The problem involves a battery with an internal resistance of 0.50 ohm and several identical light bulbs, each with a resistance of 15 ohm, connected in parallel. The terminal voltage of the battery is noted to be one-half of the EMF, prompting the question of how many bulbs are connected.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between the current in the battery and the circuit, questioning whether the voltage is equally divided between the internal resistance and the external resistance of the bulbs. There is also exploration of the implications of the voltage drop across the internal resistance.

Discussion Status

Participants are actively engaging with the problem, exploring the implications of the voltage drop and the relationship between resistances. Some guidance has been offered regarding the equality of the voltage drops and resistances, but there is no explicit consensus on the final number of bulbs connected.

Contextual Notes

There is a focus on the assumption that the terminal voltage is half the EMF, which leads to discussions about the equality of resistances and the distribution of voltage across components. The original poster's calculations and reasoning are still in progress.

Biosyn
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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 = Vemf - IR

The Attempt at a Solution



n = number of light bulbs

1/(Rb) = (1/15)n
Rb = 15/n

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

V = (1/2)Vemf
 
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What can be said about the current in the battery and the current in the circuit?
 
Villyer said:
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?
 
Biosyn said:
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.
 
Villyer said:
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!
 
Biosyn said:
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.

attachment.php?attachmentid=45321&stc=1&d=1332286941.gif
 

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