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The power rating of a light bulb indicates the rate at which that bulb emits light energy. It is sometimes referred to as the wattage of the bulb. A bulb with a greater power rating will be a brighter bulb. The power rating depends upon the bulb's resistance. But it also depends upon the voltage of the battery. These two variables - battery voltage and bulb resistance - influence the current that is in the bulb. So to summarize, the power rating of a bulb or bulb brightness can be related to the battery voltage, the bulb's resistance, and the current in the bulb.
 

There are two similar versions of this question. Here is one of the versions:

Version 1:
Circuit A and B have the same current. But the battery of Circuit A has twice the voltage of the battery in Circuit B. In which circuit will the bulb be the brightest?
 

 

What Affects Brightness?
The brightness of the light bulb in this simple circuit depends upon the resistance (not mentioned in the question) and the battery voltage (∆V).  The current (I) in the bulb depends on the battery voltage and the resistance. The current is mentioned in the question. To determine which circuit has the brightest bulb, you need to understand and apply the math relationship between power (brightness), current, and battery voltage.

 

The Relationship and Its Application
The relationship between power (P), current (I) and battery voltage (∆V) is given by the equation ...

P = I•∆V

The current is the same in each circuit; so current becomes a non-variable. In this question, it is the battery voltage that matters. As should be obvious from the equation, a larger battery voltage results in a larger power.  And it is power that indicates how bright the bulb will be. So make your decision about bulb brightness based upon the battery voltage values of the two circuits and the equation presented above.

 


 

Try these links to The Physics Classroom Tutorial for more help with understanding power and the factors that affect it:

Power: Putting the Charges to Work

Electric Power Revisited
 


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