Ranking brightness of lightbulbs in a circuit

[ikihi]

Homework Statement

In the circuit shown, all the light bulbs are the same. Why is the following statement true? :

A is the brightest. B and C are equally bright, but are dimmer than A.

https://pbs.twimg.com/media/C6GllsQVMAA4chz.jpg:large
https://twitter.com/FauxNews101/status/838133087464640513

Homework Equations

P = I * V

The Attempt at a Solution

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There is more of a voltage drop across B to C than A, so the power is less for both B and C than A since power is proportional to I and V? Since B and C are the same then they should be the same brightness because they each have the same resistance, in series?

 

[berkeman]

There is more of a voltage drop across B to C than A,

No. lightbulb A is in parallel with B+C. So the voltage drop across B is half of that across A, and the drop across C is half that across A.

Try again?

 

[ikihi]

No. lightbulb A is in parallel with B+C. So the voltage drop across B is half of that across A, and the drop across C is half that across A.

Try again?

The voltage drop of B+C equals the voltage drop of A. This is so because light bulb A equals the voltage drop across the equivalent of B+C since light bulbs in parallel have the same voltage. So B or C has half the voltage that A does; and because of that, the power for B and C is equal, but B or C is less power than A.

 

[berkeman]

The voltage drop of B+C equals the voltage drop of A. This is so because light bulb A equals the voltage drop across the equivalent of B+C since light bulbs in parallel have the same voltage. So B or C has half the voltage that A does; and because of that, the power for B and C is equal, but B or C is less power than A.

Yes, good.