Three different light bulbs of varying brightness are connected in series to a voltage source. Bulb 1 is the brightest, and bulb 3 is the dimmest. The voltages across the bulbs, V1, V2, and V3, are related by which of the following?A.𝑉1>𝑉2>𝑉3B.𝑉1=𝑉2=𝑉3C.𝑉3=𝑉1>𝑉2D.𝑉3>𝑉2>𝑉1
Question
Three different light bulbs of varying brightness are connected in series to a voltage source. Bulb 1 is the brightest, and bulb 3 is the dimmest. The voltages across the bulbs, V1, V2, and V3, are related by which of the following?A.𝑉1>𝑉2>𝑉3B.𝑉1=𝑉2=𝑉3C.𝑉3=𝑉1>𝑉2D.𝑉3>𝑉2>𝑉1
Solution
In a series circuit, the total voltage across the circuit is equal to the sum of the voltages across each component. The voltage drop across each component is proportional to its resistance according to Ohm's law (V=IR).
In this case, the brightness of a bulb is directly related to the power it dissipates, which is given by P=IV (current times voltage). Since the bulbs are in series, they have the same current flowing through them. Therefore, the bulb with the highest resistance will dissipate the most power and be the brightest.
Given that bulb 1 is the brightest and bulb 3 is the dimmest, this implies that bulb 1 has the highest resistance and bulb 3 has the lowest resistance. Therefore, the voltage across bulb 1 will be the greatest and the voltage across bulb 3 will be the least.
So, the correct answer is A. 𝑉1>𝑉2>𝑉3.
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