The brightness of a lightbulb is given by its power. P = I2R, and so brightness depends on current and resistance. If the bulbs are identical, they have the same resistance. They may not, however, experience the same current. Therefore, when you are asked to rank the brightness of identical bulbs, you are really being asked to rank the amount of current through each. This, then, is a circuit problem even though you do not need to specify the values of the currents.

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Power is a measure of the amount of energy converted per time. In this case, the electric energy of the circuit is converted to light and heat energies in the light bulbs.

At a junction in a circuit, some of the current goes through one branch and some through the other(s). In other words, the current splits and therefore is not the same throughout.

Don"t I need numbers to work this problem?

No. Even though you cannot give values for the current without knowing the size of the battery and the resistance of the bulbs, you can still talk about the current through each segment as a portion of the total current through the battery.

Because you do not need to solve this circuit mathematically, you do not need to reduce it to a single equivalent resistance. You do, however, need to track current. Using color to show portions of the circuit with the same current gives a very helpful visual.

How did you know all three of the "yellow" branches have the same current? Doesn"t the current divide and then divide again?

Yes. If you need to go through two steps to see that all three legs have the same current, that is fine. In that case (see the "Solve" page for more elaboration) you would find that twice as much current goes through the right branch (two resistors in parallel) as through the single resistor of the left branch, because resistance is less when resistors are connected in parallel. That larger current then splits equally when it comes to the second junction.

Current is not used up in resistors. Electric *energy* is converted to other forms (in this case heat and light) but the current remains the same. Therefore, any portion of the circuit where there is a single path must have the same current, even if the electrons go through a resistor before they get to that portion of the path.

At this portion of the circuit, the current has a choice--it splits across all three paths. Therefore, the current in each path is not the same as the green current. Because the resistance of each path is the same, the current through each path will also be the same. If you do not see that yet and gave each path its own color, that is fine. You will explore this more in the "Solve" step of the problem.

At this portion of the circuit, the current has a choice--it splits across the two paths. Because the resistance is different in the two paths, you expect the current in each to be different as well. Therefore, the two branches are given different colors to show that they have different currents.

The light bulbs are identical. Doesn"t that mean they all have the same brightness?

No. The brightness of a lightbulb is given by its power. P = I2R, and so brightness depends on current and resistance. If the bulbs are identical, they have the same resistance. They may not, however, experience the same current. Therefore, when you are asked to rank the brightness of identical bulbs, you are really being asked to rank the amount of current through each.

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How would I work this problem mathematically?

This is exactly the same circuit as in Circuit II. Click here to go to Circuit II and work it mathematically. To really understand the process well, take a look at both the conceptual and mathematical solutions and see that they are the same.