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In a series or parallel circuit, if two bulbs have the same resistance, do they have the same voltage drops? The problem I am asking about is below. Do A, B, and C have the same voltage drops since they have the same resistance? If so, how do I determine the current?

Problem

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Related: physics.stackexchange.com/q/55381/2451 –  Qmechanic Mar 1 '13 at 13:23
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@Qmechanic In my opinion, this question does not deserve to be closed. Jay Lee is asking generally "if two bulbs have the same resistance, do they have the same voltage drops?" and using the homework question to clarify; he does not just seek a solution to this specific problem. –  Draksis Mar 1 '13 at 14:02
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@Draksis: I'm somewhat sympathetic to your argument, so I decided to reopen it. Still, it wouldn't hurt if OP could describe in more detail his thoughts on the problem, and what's stopping him. –  Qmechanic Mar 1 '13 at 17:57
    
Beware! The OP is posting a series of homework questions from the third edition of Matter & Interactions by Chabay and Sherwood (Wiley, 2010). This one seems to be associated with chapter 20. –  user11266 Mar 10 '13 at 22:58
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1 Answer

up vote 3 down vote accepted

No, they do not all have the same voltage drop. If they were in series, however, they would.

By Ohm's Law, the voltage drop is proportional to the current flowing through a resistor. (So in several series resistors with the same resistance, the drop across each one is the same, since the current across each one is the same). However, because B and C are in parallel, the current is split between those two, meaning that the current in B and C is different from that passing through A.

However, since B and C have the same resistance, you know that the current from A is split 50/50 between them, so since each one gets half of the current, the voltage drop across each one is half of the voltage drop across A.

To find the current, first find the equivalent resistance using parallel and series resistor simplification techniques. Condense the two parallel 10 ohm resistors into a single resistor, and then combine this resistor with the series 10 ohm resistor. This tells you the total (or "equivalent") resistance of the circuit. Since you know the voltage produced and the resistance of the circuit, you can use Ohm's Law to find current.

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What if the resistance of Bulb C was changed to 50 ohms? What would happen to the currents passing through the three bulbs, voltage drops of the bulbs, and the current passing through the battery? –  Jay Lee Mar 1 '13 at 13:20
    
The process you would follow would be the same as in the last paragraph of my answer. You would find the equivalent resistance of the circuit to find the current, then use this current to find the voltage drops and currents passing through each component. –  Draksis Mar 1 '13 at 14:04
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