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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?
The diagram shows first four resistors in series then four resistors in parallel.
For the resistors in series the current flowing into the wire, $I_{in}$ must be the same as the current flowing out, $I_{out}$ because the current can't escape from the wire. There is only one route for the current to flow through the wire so the current has to pass through all the resistors in turn. That's why the current passing through every resistor must be the same.
Now look at the resistors in parallel. The point here is that the top ends of the resistors are all connected together so they must all be at the same voltage $V_{in}$. Likewise the bottom ends are all connected together so they must be at the same voltage $V_{out}$. That means all the resistors have the same voltage drop across them of $V_{in} - V_{out}$.
The starting point of this question makes it hard to give a short, satisfying answer; maybe someone will come along and do a standout one with diagrams, but I don't have time for it. So I'll kick off with this:
With two resistors in series, there's more total resistance on the circuit, which means that less current flows. With less current flow, a given resistor drops less voltage because V=IR. Voltage drop isn't an intrinsic property of the resistor; resistance is.
Best Answer
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.