Common Misconception 1: The Effects of Resistors on Charge Flow
We typically come to our first course on the analysis of electric circuits with some vague ideas about how circuits work. In many cases our ideas are based on common misconceptions; these misconceptions represent significant obstacles to mastering the subject. This brief reading exercise considers one of the common misconceptions beginning students studying circuits often exhibit. The hope in investigating this misconception is to help you form proper mental models for how circuits behave at a macroscopic level. The microscopic behavior of electrons in a circuit is complicated and we only touch on it here. Expect to discuss such issues in more depth in your physics courses.
Consider the circuit of Figure 1 that consists of an ideal independent voltage source, two incandescent light bulbs, a resistor, and wires connecting the elements into a single-loop circuit. There is clearly only one path for charge to flow.
Figure 1: A series circuit with an ideal independent voltage source, two identical incandescent light bulbs, and a resistor.
Before we proceed further, please answer the following question.
Which bulb is brighter?
The two identical bulbs of the circuit shown in Figure 1 will be of the same brightness. Why then do many students beginning the study of circuit analysis think that bulb 1 will be brighter than bulb 2 in the circuit of Figure 1? Most have an idea that a resistor hinders or reduces current. In a sense this is true, but how does this happen and what does this truly mean? Does the resistor consume charge? Does the resistor consume current? Does the resistor cause charge to build up? We begin to address these questions within the next tabs.
Let’s consider Figure 2 that is a single ideal voltage source connected to a resistor, thus forming a single loop.
Figure 2: An ideal independent voltage source connected to a resistor forming a single-loop circuit.
With but a single battery and a single resistor in a loop, we feel confident that electrons tend to move counterclockwise in the circuit, being attracted to the positive end of the battery and repelled by the negative. This is a simplistic view, and while useful with such a basic circuit, this view can cause trouble when things get more complicated. How should we think of things then?
We know that the voltage source is a source of potential difference; its positive terminal is higher than its negative terminal by VS volts. This potential difference induces an electric field in the circuit whereby surface charge along the wires redistribute. The redistributed surface charge along the wires creates an electric field within the wires that in turn, causes charges within the wires to move. That is, redistributed surface charge on the wires creates an electric field along the wire to provide the “push” to move the electrons. This redistribution of surface charge happens extremely rapidly (scale of nanoseconds) as only a subtle movement of surface charge is necessary to establish the electric field to move free electrons along the wire. When flipping a light switch, the lights in a room turn on almost instantaneously. Why? Electrons do not need to travel from the light switch to the bulb, rather, surface charges rapidly redistribute throughout the circuit creating electric fields along the wires that “push” the free electrons that already exist everywhere in the conductors and filament of a light bulb. Similar arguments apply whether the lights are old-fashioned incandescent bulbs or modern light emitting diode (LED) lights. Click on the next tab to continue.
OK, so the redistributed surface charge induces electrons within the conductor to move. But what do the resistors do? Let's imagine that electrons are traveling along the inside of the wire in a clockwise direction and focus on those approaching the resistor of the circuit depicted in Figure 3.
Figure 3: An ideal independent voltage source connected to a resistor forming a single-loop circuit.
Does the resistor consume some of the charge that enters it, thus "resisting" charge flow to a degree proportional to its resistance?
What if the resistor just slows electrons down such that fewer leave the resistor per unit time than enter?
Figure 4: An ideal independent voltage source connected to a resistor forming a single-loop circuit.
Figure 4: The circles with the negative signs are cartoon representations of free electrons that would actually be inside the wires and resistor. Remember that there are free electrons throughout the circuit. We know electron motion is counterclockwise in this circuit and that resistors “resist” charge flow. Do electrons therefore build up within the resistor such that more electrons enter the resistor than leave as suggested in the cartoon sketch? Click on the Figure 4 once again to find out.
Figure 4: The circles with the negative signs are cartoon representations of free electrons that would actually be inside the wires and resistor. If electrons did build up within the resistor, the amassing collection of electrons would eventually repel additional electrons, and electron motion would cease.
If the charges continued to build up within the resistor, eventually they would build up to a point at which additional charges would be repelled and charge flow would cease. Since current is a measure of charge flow, current would therefore go to zero. This would suggest that the light bulbs of Figure 1 would illuminate only briefly, or perhaps not at all. This is contrary to what we know will happen with the light bulbs. What does the resistor do that impacts charge flow?
As noted previously, the voltage source induces the redistribution of both positive and negative surface charge along the wires in the circuit. This surface charge establishes the electric field along the wires which in turn induce electrons to flow. Resistors neither cause the free electrons to continuously build up to the point at which current ceases nor do resistors consume charge. We therefore should feel comfortable that the net time rate at which electrons flow into a resistor is the same net time rate at which they flow out of the resistor. The time rate of charge flow past a point in the circuit is just the current at that point in the circuit. Since current is defined as the flow of positive charge, current is directed clockwise in all the circuits we considered so far. That is, current is directed opposite of electron flow. Examine Figure 5 which is a schematic of a circuit we have considered before, but now a few currents are labeled.
Figure 5: A series circuit with an ideal independent voltage source, two light bulbs, and a resistor. What can we say about the relative values of currents I1 through I4?
In the circuit of Figure 5, we know that the net motion of electrons is counterclockwise and so conventional current is clockwise. Based on our previous discussion, select the appropriate option regarding the relative values of currents I1 through I4.
What are the relative values of current in this circuit?
Let’s put into practice what we have learned about single-loop circuits as it relates to the flow of charge. Consider the circuit of Figure 6 in which an ideal independent voltage source is connected to two resistors of unequal value, with one being three times the resistance of the other.
Figure 6: A series circuit with an ideal independent voltage source and two unequal resistors.
If I1 = {I1} A, what is the value of I2? Note that the second resistor has three times the resistance of the first resistor.
If the current is the same everywhere in the circuit of Figure 6, how do the different valued resistors impact the behavior of the circuit? Notice that Figure 6 now labels the voltage drops across the two resistors. Since we know that the current is clockwise in the circuit and that resistors always obey the passive convention, the voltage drops across the resistors must have been established with the depicted polarity to set up such a current. Before finishing out our discussion, let’s answer a few more questions.
Assuming that V1 = {V1} [V], what is the value of V2 in volts?
Given that V1 = {the value that had been used before} and V2 = {the correct answer}, what must the value of VS be?
Two more questions and then we will summarize a few key points.
So we have found that the VS = {correct answer} [V]. Let’s say that we leave the voltage source and the resistor R, but change the 3R resistor to 4R. Will the current, I, increase, decrease, or remain the same as compared to that in the original circuit?
What will be the voltage drops V1 and V2 be in this case with the R and 4R resistors? Round your answers to one digit after any decimal point.
That's correct! Let's summarize a few things we have discussed.
1. Resistors neither consume free electrons, nor do they allow free electrons to continuously accumulate and stop current.
2. The net rate at which charge enters a resistor is the same as that which leaves the resistor.
3. In a single-loop circuit, the current is the same throughout.
4. What causes free electrons in a circuit to move? In the circuits we have considered, the single voltage source facilitated the rearrangement of surface charge along the circuit’s wires and the resistors. This surface charge induces an electric field along the wires and resistors that provides the “push” for free electrons to move in a given direction.
5. If two unequal-valued resistors share the same current, the potential difference (i.e. “voltage drop”) across the larger resistor must be higher, thus maintaining equal current.
6. The rearrangement of surface charge in a circuit takes place extremely rapidly with a time scale on the order of nanoseconds.
There is perhaps still a bit of a mystery to resolve. While resistors do not consume charge, when they have a potential difference across them, they do “expend” energy provided by a source. The energy from the source is transformed to thermal energy as the electrons traveling within the resistor suffer many collisions with the atoms comprising the resistive material and thus heat the resistor. An old-fashioned incandescent light bulb itself may be modeled as a resistor. When illuminated, such a light bulb transforms energy from a source to both heat and light. Efficient light bulbs transform more of the energy provided by a source to light rather than to heat.
Congratulations, you have completed the reading application. Click the PDF button to create a brief report of your trip through the application.
What remains the least clear idea in the reading for you? Thoughtfully responding to this question will help guide revisions to the writing exercise and remind you to seek clarification of this point.