Ranking Brightness of Lightbulbs in a Circuit

[leonardthecow]

Homework Statement

Consider a circuit containing five identical light bulbs and an ideal battery. Assume that the resistance of each light bulb remains constant. Rank the bulbs (A through E) based on their brightness.

http://postimg.org/image/5dlx5a1p3/

Homework Equations

V=IR => I=V/R

The Attempt at a Solution

I understand that brightness is proportional to the current. I also know, by this logic, that the brightness of A is the same as the brightness of B, because the current "splits" and the resistances of both A and B are the same. Therefore, I=V/R for each.

Moving on to C, D, and E, I see that the same total current that splits to go through both A and B now splits again to go through C, and through D and E. D and E are in series, so their equivalent resistance is R + R = 2R. So the current through the D/E side of the split is I=V/2R.

I know that the total current that split between A and B initially is I=(V/R)+(V/R)=2V/R. So the current through C must be (2V/R)–(V/2R)=3V/2R.

Ordering the brightnesses of the bulbs, I then come up with C>A=B>D=E.

Is this correct? I struggled for a long time through this, and it wasn't very intuitive for me. Are there any "tips" that anyone has for thinking through these types of problems in general?

Thank you in advance!

 

[SammyS]

Homework Statement

Consider a circuit containing five identical light bulbs and an ideal battery. Assume that the resistance of each light bulb remains constant. Rank the bulbs (A through E) based on their brightness.

http://postimg.org/image/5dlx5a1p3/

Homework Equations

V=IR => I=V/R

The Attempt at a Solution

I understand that brightness is proportional to the current. I also know, by this logic, that the brightness of A is the same as the brightness of B, because the current "splits" and the resistances of both A and B are the same. Therefore, I=V/R for each.

Moving on to C, D, and E, I see that the same total current that splits to go through both A and B now splits again to go through C, and through D and E. D and E are in series, so their equivalent resistance is R + R = 2R. So the current through the D/E side of the split is I=V/2R.

I know that the total current that split between A and B initially is I=(V/R)+(V/R)=2V/R. So the current through C must be (2V/R)–(V/2R)=3V/2R.

Ordering the brightnesses of the bulbs, I then come up with C>A=B>D=E.

Is this correct? I struggled for a long time through this, and it wasn't very intuitive for me. Are there any "tips" that anyone has for thinking through these types of problems in general?

Thank you in advance!

(It seems that one sketch of the circuit with all the bulbs labeled would have been preferable. I realize this figure was not your doing.)


Your analysis is perfectly fine -- probably the most concise way to get the correct answer.