Tuesday, April 5, 2011

AP Series Parallel Lab

I just finished grading the series parallel labs for AP 4. Every single one of them got most of the questions wrong for parallel circuits and AP 5 wasn't much better. If two bulbs or other resistances are are in parallel they see the same voltage. The current expected in each resistor or bulb is found by dividing that voltage by the resistance of the resistor in question. There is no consideration of the other parallel resistances in this process. As long as the voltage is not altered the current in resistor 1 does not vary regardless of the value of or even existence any other resistor in parallel to it. All of you used this valid approach in calculating the currents in the resistors in part B. Yet when asked what happens to current in a resistor when another parallel resistor was removed, you all incorrectly assumed that the current from the removed resistor still existed and now how to travel through the remaining ones.

The fact that you combine this unfounded and incorrect assumption about current remaining when the element through which it flows is gone with the [correct] way you predicted the current in parallel resistors [where the current through resistor 1 is calculated without any reference to resistors 2 s value or existence or the current that might or might not flow through resistor 2] in the same lab shows you are still not thinking analytically.

Let me put it numerically. I have resistor 1 of 40 ohms with 20 volts across it. A current of 0.5 amps flows through it. I now connect resistor 2 of 20 ohms in parallel with it. Resistor 2 sees the same 20 volts across it and produces a current of 1 amp, while resistor 1 produces the same 0.5 amps. I now disconnect resistor 2 and have resistor 1 in the exact same circumstance it originally was in. Now you are telling me that even though everything is the same as before, it will produce more than 0.5 amps and you would probably say 1.5 amps. I hope by now you realize this makes no sense.

You all should know that the voltage drop across an element [ bulb, resistor, etc.] causes the conduction electrons in that element to move. If you remove that element those electrons are no longer there, the current they provided is gone. The only reason removal of one parallel resistor would increase the current in the other remaining parallel resistors is if there is another resistance in series. In this case, the reduction in current due to the removal of the parallel resistance would reduce the current through the series resistance. This would reduce the voltage drop through the resistance in series, leaving more voltage drop available for the remaining parallel resistances causing an increase in their current. This increase is only very indirectly related to and certainly not equal to, the current that used to flow in the removed resistor.

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