Topic open: Circuits

The following topic is now open for questions: Circuits. Anything about resistors, capacitors, RC, RL, RLC circuits.

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Question: Current and a switch

I'm just wondering. If there is an open switch AFTER a resistor, the current still goes through the resistor but does not continue in the circuit, right?

If there is an open circuit, there is no current flow. For current to flow there has to be a continuous path from a high potential to a low one, otherwise charge would have to build up somewhere... which cannot happen. If the charge built up in this way, the charges flowing in behind them would feel more and more repulsive force until the potential required to pile in more equaled the potential of the battery and there was no driving force left. This is basically what happens in a capacitor, and a real circuit will have some of this occuring, but the end result in both cases is that the current stops flowing.

Ever been on a really crowded bus? There is somewhat of a driving force from the front of the bus to the back of the bus as people get on and the bus driver yells to everyone to go to the back. As the bus fills up, and fills up, people at the front push people in the middle who push people at the back closer and closer together, but eventually there is nowhere for them to go... at some point, the flow of people towards the back has to stop until people get off and make room again.

A wire is like an already crowded bus. The charges close to the battery (the front of the bus) feel a driving force from the battery, those charges move slightly, and because they are displaced in the wire, there is a net charge which repels like charges near them and pushes them ahead a bit. This continues all around the wire. But, if there is a break in the loop, there is nowhere for the charges to go (they can't just jump out of the wire), so they just sit there and wait until there is a way for them to move.

The short answer to your question is: if there is an open switch anywhere in a loop, there will be no current flowing through any part of that loop. If there are alternate closed paths in the circuit, then current can flow through those parts of the circuit, but they must constitute a closed loop, with some source of potential a.k.a. electromotive force (EMF) (a battery, DC or AC power supply, a charged capacitor...).

Hope this helps. Please post a comment to this if you need clarification

Topic open: Anything DC circuits

The following topic is now open for questions: Anything DC circuits. Including: Resistor networks, Kirchoff's laws, Capacitor networks, RC circuits...

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Question: Using loop rules (Chapter 19 #29)

I am stuck at # 29 (chapter 19) and I really don't know where I went wrong. I made 2 loops, 1 with R1 R2 and another with R2 and R3 and then I had one junction equation.

Well, from what you said it seems like you are on the right track. Using two loop rules, and one junction rule, I get the following equations:

loop 1: E1-I1R1-I2R2=0 loop 2: E2-I2R2-I3R3=0 junction: I1+I3=I2

This does give you 3 equations with 3 unknowns. Solving these systems by substitution can be a bit tricky, but with perserverance can be done. I show an example on the help home solving both by substitution and a matrix method (which can be a quick way to solve if you have access to a graphing calculator, or are good with matrix reduction). To see the example and a review of Kirchoff's laws go to: Kirchoff's laws and their application.

Let me know if these are not the equations you got, and we will backtrack some more and find out where the problem is. (Remember, you can post follow-up questions as comments to this post.)

Question: Adding another resistor

I was wondering if you could tell me if, say you have five resistors in a circuit, and you add another one, does the power of the battery have to increase? Or does the system just slow down or something...

Ok, I'm first going to have to clairfy and simplify the system we are talking about. I'm going to reduce the problem to a battery and a resistor. The only difference in having 5 as opposed to 1 is reducing that network of 5 resistors. We will also assume that we have a battery providing a constant voltage source (this is the normal case), and that it can provide whatever current we demand of it (it has no maximum current output).

So, let's take our battery and resistor. Using Ohm's law, we can determine that the current is I=V/R (if we had 5 resistors of equal resistance in series to start the current would be I=V/5R since the equivalent resistance of those 5 resistors in series would be 5R). And then the power drawn from the battery would be P=IV, or P=V²/R.

Now suppose we add another resistor, of equal resistance, in series. The equivalent resistance of the two resistors would be 2R, and the new current would be I=V/2R, and the new power would be P=V²/2R (if we had added one more in series to our 5 resistors we would have I=V/6R, and P=V²/6R).

The voltage provided by the battery does not change due to the addition of another resistor, however the power output decreases (because the current drawn decreases).

We can go through the same analysis assuming the resistors are in parallel. The current with just one resistor is I=V/R, and power is P=V²/R. If we add a resistor in parallel, the current will become I=2V/R, and the power will be P=2V²/R. Here, again the voltage of the battery does not change (it is a constant source of potential), but the addition of another resistor in parallel increases the current drawn from the battery. Since the current increases, the power supplied by the battery also increases.

So, what happens when we "add" a resistor to a circuit? That depends on how we add the new resistor. The voltage provided by the battery stays constant in all cases. The current may change depending on the arrangement of the resistors. To determine how the current will change you must reduce the resistor network before and after adding in the new resistor, and use Ohm's law to determine the current before and after. If the current changes, the power will change, since Power is proportional to current. Again, compare before and after to determine the change.

Finally, let's be clear about the difference between "voltage" and "power". Voltage, or potential difference, is increase/decrease in potential energy per unit of charge. Power is the energy per unit time, in this case electrical energy per unit time flowing through the circuit. It is the battery which supplies both. That energy has to come from somewhere, right? You can think of power as being an energy transfer, the battery is providing energy at some rate to move charges around the circuit, at some rate.

Hope this helps clarify some things. You might also be intrested in a previous student's question on Voltage, EMF and resistors (about half way down the page). Let me know if this answers your question or not (by posting a comment to this post).

Topic open: Resistor networks

The following topic is now open for questions: Resistor networks.

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