Mood Brightener: ...more from Stay Homas. (Confination XI)

Your Conceptual Goals for this section: Circuit Concepts

Applied Electrodynamics (not so static):

This is otherwise known as electrical circuits. We will start by working extensively with conceptual circuits before we move to the standard calculational approach. There are deep reasons why we do this that mostly relate to challenges students routinely face in future classes when they haven't internalized the conceptual framework of circuits.

The Basic Elements:

The basic elements of circuits are sources, connectors, and loads. Sources put energy into the system that is carried by moving charges to deliver that energy to loads. Loads are any one of a number of devices which use the energy in the circuit to do useful and interesting things for us. Connectors are switches and wires and other devices that help us direct the energy carrying charges where we want.

Connectors:

What is a typical connector for electrical systems that you have seen? Is it the same inside your calculator? How about in a solar panel?

You are likely to think of wires or conductors as the connector for electrical systems. Why do we use 'conductors'? What is the feature of conducting materials that is relevant? What is the sign of the charge that moves? Why?

Applying our existing conceptual tools:

What makes the charges move (that we have been talking about for weeks)? Draw a large straight chunk of wire. Which charges in the wire move? Is there a net charge 'in' the wire? Indicate which way you are assuming the charges move and then illustrate what you mean. Does your choice of E field correctly explain the direction of movement of your chosen charge?

Do you think of the wire as completely full of charge like a highway full of cars or an empty road waiting for traffic?

What if the wire has a corner in it? How does one produce an E field like this?

Didn't the instructor say that the E field inside a metal object was 0? What were the special conditions of that statement?

If there is an E field running the length of the wire what does that mean about the potential difference between the ends? Which end is at the higher potential? Is that consistent with the direction you have your charges moving?

Sources:

Hopefully, as a result of the previous explorations, you have come to the conclusion that if I can make an E field in the wire then the (-) charges that are already there will begin to move. If there is an E field in the wire then there must be a potential difference between the ends of the wire. If we can create a potential difference between the ends of the wire then the rest of the behavior follows.

This raises the question of how do we create that potential difference? That's actually a pretty significant question but let's just say that the chemists have figured out one way to do this which we call a battery.

A battery is a chemical factory which can lift charges up the energy hill to a particular voltage. To be more careful the basic unit of this chemistry set is called a cell and has a characteristic potential difference that depends on the specifics of the chemistry set. A lead - acid cell creates a potential difference of just over 2 V. An alkaline battery creates just over 1.5 V for each cell. Lithium ion cells are around 3.6 V. We can combine cells together to get batteries like the 12V car battery that is 6 lead-acid cells in sequence. Imagine each cell lifting the charge up 2V and then handing it off to the next cell for another 2 V until you get to the 'top' at 12V.

At this point there are a number of interrelated concepts that you might have that are inconsistent with each other and I am always of mixed minds (as if I had more than one) about which way to approach this.

A Series of Thought Experiments: I

If I attach one end of a length of wire to one end of the battery what do you think will happen?

Consider: Will there be a potential difference between the ends of the wire? If there is will there be an E field? If there is an E field do charges move in the wire? Where do they go? IF you think there is NOT a potential difference can you explain why? If there is no potential difference will charges move?

A Series of Thought Experiments: II

If I attach one end of the wire to the (+) potential end of the battery and the other to the (-) potential end what do you think will happen?

Consider: Will there be a potential difference between the ends of the wire? If there is will there be an E field? If there is an E field do charges move in the wire? Where do they go? If the charges enter one end of the battery what is happening at the other end of the wire? What does this suggest is happening inside the battery? Is charge disappearing or just circulating from place to place? Where is energy given or taken from the charges?

Class Discussion:

What is the net charge in the battery at any moment? In the wire? How does a battery 'run out'? Run out of what? (This is explored to some extent in electrochemistry in CH222 and CH223)

Volta of twitching frog legs fame was one of the early experimentors in this field. How did he make his battery?

Here is the standard symbol for a battery (DC voltage source). We'll worry about AC later (maybe)

Loads:

Loads are a generic term for things which use the energy which is flowing through a circuit. They often have two terminals but sometimes more. Lights, speakers, sensors, and motors are all examples of loads. For now we are going to use light bulbs to represent loads.

Circuits:

What's inside a light bulb? What does it mean to connect a light bulb in such a way that it will light up? Imagine you have a 12V light bulb from a car, a car battery, and a couple of wires. How do you hook everything up so the light bulb will light up? Can you find some different ways to do it? What if you only had 1 wire? Two wires and two bulbs?

Is this what you were imagining for the structure of a light bulb?

In order for a circuit to work there has to be a continuous pathway for the charges from the high potential to the low potential.

A Series of Thought Experiments: III

So lets consider this circuit which has all the basic elements we've been talking about. The battery which raises charges up the potential hill, the bulb which extracts energy from the system to make light, and the conductors which allow the charges to move from the battery to the light (and back?).

Sketch this circuit and assume the it's a 12V battery and 100 charges per second pass a point in the circuit after the switch is closed. These numbers are just place holders not meant to represent some ultimate reality. With the switch closed indicate which way you think the charges are moving, how many pass into and out of the battery and the lamp, and what the potential of the charges is as they enter and exit the battery and the lamp? For the purposes of this exercise we will assume that the charges can move easily through the wires and lose no energy. You should end up with a very busy drawing that we can use to firm up our understanding.

 

Class Discussion:

I am loathe to put any conclusions in here since they might derail your own examination of your thinking. Perhaps I will update this later.

Terminology: Current

If we connect two ends of a conductor to a high potential and a low potential respectively the there will be a field and charges will begin to move. Do they accelerate or move with constant velocity? If you think they move with constant velocity how to you explain that given the electric force the charges experience Newton's Law says they should accelerate?

The movement of charge is called current (symbol I or i) and it is defined to be the amount of charge passing a point in the circuit in some period of time. I has units of C/s which we call Amps (A). Be sure to notice that 1A is a huge amount of charge in motion (an entire lightning bolt!)

Notice that charges flowing in a circuit are going 'uphill' or 'downhill', depending on how you think of it, which means potential energy is being extracted. What is our expression for electrical potential energy? (PE_E = qΔV!)

Power:

Power is the rate at which energy is delivered (dW/dt or ΔW/Δ t). In this setting each charge is delivering some energy to the bulb. That means the rate a which energy is delivered depends on I (# charges/s). In addition it must depend on how much energy the charges leave behind (ΔV)

What do you get if you multiply I*ΔV (look at the units!)? Hopefully you find that the units are J/s = Watts (W) which is power! Power is the rate at which we are delivering energy.

Terminology: Resistance

Every part of a circuit impedes the flow of the charges to some extent. Resistance is the name we give to this characteristic of materials. Connectors (wires) are generally assumed to provide essentially no resistance - very much like ideal frictionless surfaces last term. Loads are considered to be the primary source of resistance in a circuit.

Summary:

Here are the core ideas that we hope to take away from this exploration:

Current is the same at every point in the circuit! Charge is not 'eaten'.

All the voltage drops occur across loads and not across wires.

More potential difference (steeper energy hill) might be associated with more current flowing.

Greater resistance means less current flow all other things being equal.

Higher watt bulbs have less resistance and allow more current to flow.

Taking it up one step:

Take the circuit we explored in Thought Experiment III as a reference and then consider these circuits. Assume identical bulbs and batteries in all circuits.

What can you say about the relative brightness of the (identical) bulbs in each of these circuits? Consider what the voltage drop is across each bulb and what that indicates about the current. Remember that energy consumption (power) is current times voltage (P = I*ΔV).

Series and Parallel:

The bulbs in circuit I are considered to be in Parallel in that the current flows through each before rejoining. The bulbs in circuit II are considered to be in Series because the current must flow through them sequentially.

Note that when bulbs are in parallel they each (all) have the same voltage drop. Bulbs in series must have the same current flowing through them.

Update to the core ideas:

A couple core ideas listed above will need an update based on this most recent discussion.

Current is the same at every point in the circuit! Charge is not 'eaten'.

becomes....

Current is the same at every point along an individual branch. Where multiple wires come together the current will divide or recombine. Charge is not 'eaten'!

More potential difference (steeper energy hill) might be associated with more current flowing.

becomes....

More potential difference (steeper energy hill) across a load leads to more current flowing.

This raises an important conceptual question. If the wires are all the same size what does it mean to say the current divides? The language of 'dividing' suggests fewer charges are moving in each wire after a junction but is that consistent with model? How can we have less current with the same number of charges? (charges slow down) Regardless of this the lanugage that is customarily used is 'less' current flows in each branch after the junction. We have to understand that current is NOT the number of charges but the number of charges passing a point in the circuit.

A Totally Relevant Question:

What happens in each circuit (series and parallel) if the filament in one of the bulbs breaks? What does this suggest about your house?

Anybody have an old set of Xmas lights? What about them?