Resistors

[nc2tarheels]

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It's been around a year since my physics II class. Here's my problem, I remember that resistors in parallel can be added together (1/r + 1/r) = 1/r. And I understand the V=IR, however, let's say two resistors are in parallel (2 ohms and 4 ohms). I know that more will flow through the 2 ohms resistor. How do you tell what the current/voltage is that flows through the 2 ohm resistor is? Thanks!!

 

[Rabolisk]

All circuits are based on the Kirchoff's circuit laws, which can be summarized as junction and loop rule. If two resistors are in parallel, then, by definition, they form a closed loop, and the potential drop across each have to be equal. That is, V(1) = V(2) = Veq

I would first find equivalent resistance. You are either going to be given V (through EMF, this may take some manipulation if there are other resistors in the circuit) or I (total current through the resistors). Realizing that V across the equivalent resistor is the same as V across each resistor, now you can apply V=IR to each resistor to solve for I(1) and I(2).

As a note, the formula 1/R1 + 1/R2 = 1/Req is based upon Kirchoff's laws (which themselves can be proven, but that's way beyond scope), which are fundamental to circuits. I would memorize that series = same I and parallel = same V.

 

[plzNOCarribbean]

Another shortcut to finding the equivalent resistance is to use the Product over sum rule; it is quicker. This however, only works for TWO resistors in parallel at a time; if there are more than two in parallel, you must use the other equation or simplify the parallel resistors TWO AT A TIME;

After finding Req, Divide the total voltage by Req to get the total current (V/Req=I); Then, because we know the simplified combination of the parallel resistors, multiply the current by the Eq resistance of the parallel combination to find the voltage drop across that element; the voltage drop will be the same for both resistors in parallel, as mentioned about;

Then, to find the current flowing through each resistor in parallel, divide the voltage drop by their resistance; the sum of their currents should add to the total current flowing through the circuit.

Also, remember that when resistors are in parallel, the equivalent RESISTANCE IS ALWAYS LESS than the resistance of each of the resistors separately; Conversely, when the resistors are in parallel, the Equivalent resistance is ALWAYS greater than the individual resistors;

^For Capacitors in parallel, the Total Capacitance is always GREATER when the capcitors are in Parallel; that is, Capacitors in Parallel are like RESISTORS ARE IN SERIES (ie capacitance Increases, like how Resistance Increases); And capacitors in series, the capacitance is always LESS, like resistors in Parallel

Hope that helps; if anyone see's any mistakes/flaws in my logic, please let me know; my test is in a WEEK!