Electric Circuit Model Reading

Electric Circuit Model Reading

Section 1Circuit representations:

Definition of circuit
Acircuitis a continuous conducting loop including something to push charge through the circuit (like a battery or a generator). Aclosed circuitis one in which charges are flowing. Anopen circuitis one that has an intentional break in the loop, usually with a switch. Ashort circuithas a low resistance path that may bypass elements in a circuit and allow huge amounts of charge to flow in the circuit (dangerous).

The circuit on the left is a closed circuit; charge flows around the complete loop and the bulb lights. The middle circuit is an open circuit since the switch has broken the path so charge cannot flow and light the bulb. The circuit on the right is a short circuit. Charge will not flow through the bulb since the direct conducting path between the battery terminals has much less resistance. Since the resistance is so low, huge amounts of charge will flow, making the wires hot and quickly wearing out the battery.

Physical layout vs. schematic diagram
A physical layout diagram shows the actual arrangement of elements in a circuit as if a picture had been taken. A schematic diagram uses symbols for circuit elements and the lines connecting elements show direct electrical connections. These may or may not be wires. For example, in the left schematic diagram above, we don’t know if there is a wire attaching the bulb to the positive terminal of the battery or if the bulb is actually touching the battery.

Section 2Charge flow model:

Charges move through conductors due to electric attraction and repulsion.
A battery is a device that uses a chemical reaction (oxidation-reduction) to separate charge. When the battery is connected to a circuit, charges flow from one terminal to the other to neutralize the charge. The conventional definition for the flow direction is positive charge flowing away from the positive terminal toward the negative terminal. (This definition was proposed before the electron was discovered, and since it works, it is still used today.)

Charges do not get “used up” in a circuit
Charges are not created or destroyed (conservation of charge) so it is important to picture them as little particle-like objects that flow in and out of circuit devices. The charges themselves do not make bulbs light. We will see later that it is the energy that each charge carries that lights the bulb.

Adding obstacles inhibits the flow of charge (series circuits)
A series circuit is one that consists of a single loop. In a series circuit the charge flows equally through each circuit element, and equally through each wire. (Your evidence that the current flow is equal everywhere in a series circuit was the observation of equal compass deflections under each wire.)
In a series circuit, when more obstacles are added it is harder for charges to flow, and as a result the flow rate decreases. Each obstacle (like a lightbulb)resiststhe flow of charge and has a measurable property calledresistance. Charge flow is inversely proportional to resistance.

In the three series circuits above, we can see the inverse relation between charge flow and resistance. The left circuit is our reference circuit. The middle circuit has twice the resistance of the left circuit, (assuming the bulbs have identical resistance) therefore the middle circuit has only half the charge of the left circuit. The circuit on the right has three times the resistance of the left circuit and has one third the charge flow from the battery and through the circuit. A visual indicator of the charge flow is the brightness of the bulbs. As the charge flow increases, so does the brightness.

Adding pathways allow more charge to flow (parallel circuits)
Aparallel circuitconsists of more than one loop. This means that the flow of charge is not equal everywhere in the circuit, since there will be junctions where the charges split to take different paths around the circuit.

Note that the parallel circuits above right are identical since they both show the same electrical connections. Both show that the charge flowing from the battery splits, some travels through each bulb, the charges rejoin and flow back into the opposite terminal of the battery.
Adding additional pathways (branches or loops) to the circuit makes it easier for charge to flow since there are more ways to make it around the circuit. In parallel circuits, each branch is also independent of one another. Each branch can be turned on or off without affecting the operation of the other branches. (This is why your house is wired in parallel.) However, changing the branches does affect the charge flow from the battery. The more branches that are added, the more quickly the battery will die (be unable to separate charge via chemical reactions).

In all three circuits, the bulb brightnesses and the flow of charge through each branch are identical. The flow of charge from the battery is not identical. If the flow in the left circuit is X, then the flow from (and into) the battery in the middle circuit is 2X. In the right circuit the flow would be 3X, as long as all of the bulbs have identical resistance.

Current (in Amperes) is defined as the number of charges (in Coulombs) flowing past a point each second
Electrical current is the fancy name for "rate of flow of charge". One Coulomb of charges (which is 6.25 x 1018electrons) passing a point in a wire in one second is one Ampere of current. The common abbreviation for current in equations is the capital letter "I" to minimize confusion with Coulomb, charge, and capacitance. The unit for current, Ampere, is abbreviated "A".

Junction rule: (conservation of charge)
In parallel circuits there are junctions where the charge flow splits or rejoins. The number of charges flowing into a junction must equal the number flowing out of the junction. In other words, the sum of the currents entering the junction must equal the sum of the currents leaving the junction.

The resistance of each branch determines how the current will split when it gets to a junction. More current will flow along the branch with less resistance.

In the circuit above, the charges will split unevenly at the junction. Twice as many charges flow through the single bulb branch as flow though the two-bulb branch. For example, 3 Amperes of current might flow out of the battery. The current would split at the junction so that 2 A travels through the single bulb and 1 A would flow through the two-bulb branch. The current would rejoin at the other junction and 3 A would flow back into the battery.

Section 3Charge energy model:

Each charge carries energy
Charges carry electrical potential energy and recalling gravitational potential energy is very useful in visualizing their energy. Lifting a brick farther away from the earth changes its gravitational potential energy even though the brick is physically unchanged. In a similar way, positive charges near the positive terminal of the battery have moreenergy than charges near the negative terminal of the battery. With gravitational potential energy, we were free to define ground level so we became interested in changes in potential energy. Electrically we are also interested in potential differences, which tell us how much energy each charge transfers to the circuit element. The potential difference of the battery tells us the maximum energy per charge the battery can supply.

The diagram at right illustrates the analogy between gravitational and electric potential energy. Gravitational potential energy depends on the position of the mass in the earth’s gravitational field. Electrical potential energy depends on the position of the charge in the battery’s electric field. An important difference is that in the electrical case physical distance is unimportant. Charges lose very little of their energy as they pass through connecting wires. They lose much more energy when they pass through circuit elements that have resistance. When the charges reach the opposite terminal of the battery, they have reached their lowest potential energy.

Voltage is defined as the number of Joules of energy for each Coulomb of charge
The idea that each energy carries charge is very useful, so the ratio of energy per charge is given a name,voltage. When energy is given in units of Joules and charge in units of Coulombs, the voltage is in units of Volts. For example, a 1.5 volt battery supplies 1.5 Joules of energy to each Coulomb of charge. Potential difference, the amount of energy each charge transfers to a resistive circuit element, is also measured in volts. For example, charges flowing in a series circuit with two identical bulbs in series connected to a 1.5 volt battery will transfer half of their energy to each lightbulb. The potential difference across each lightbulb is 0.75 V.

Charges transfer energy to obstacles
When charges pass through obstacles (resistance) in a circuit, they transfer some of their energy to the obstacle, causing it to heat up or light. It is as if the toll the charges have to pay to go through a resistor is some of their energy.

A circuit with an incandescent light bulb would have an energy diagram like the one above. The electrical energy carried by the charges is transferred to the bulb as heat and light.

Increasing the energy per charge increases the flow of charge: current is proportional to voltage
When batteries are connected in series, there is a larger potential difference than when a single battery is used. Since the charges carry more energy, two things happen. First, more charges are able to "pay the toll" and pass through resistive devices (the current increases). Second, each charge will transfer more energy to the devices they pass through.

The circuit on the left will light the bulb. In the middle circuit, there are two batteries. The voltage is doubled and the current will double, lighting the bulb more brightly. The circuit on the left has triple the energy per charge (voltage) of the circuit on the left, and three times as many charges will flow through the bulb on the right each second. The current is directly proportional to the voltage.

Loop rule: the energy per charge of the battery equals the sum of the changes in energy per charge around a circuit loop (conservation of energy)
Another way of stating the loop rule is the potential difference (voltage) of the battery equals the sum of the changes in potential (voltage drops) across the elements in a circuit loop.In this first pair of examples, note the new information in the schematics. The squiggly line represents a generic resistor (like a light bulb or heater). The unit for electrical resistance is the Ohm and the symbol for ohms is the Greek letter omega,W.

The series circuit on the left has a 12 Volt battery. As the charges pass through the resistors, they will transfer half of their energy to each. So the voltage drop across each resistor is 6 Volts. The loop rule is satisfied by 12 V = 6 V + 6 V.

In the parallel circuit on the right, both resistors have direct electrical connections to the battery, and both resistors are in their own loop. The voltage of the battery has to be equal to the voltage drop across each resistor, regardless of its resistance, since a charge will give all its energy to one resistor as it passes through a branch. Here we use the loop rule twice: 12V across the battery = 12 V across the left resistor and 12V across the battery = 12 V across the right resistor.

Now we will look at the loop rule when the resistors do not have equal values. In the series circuit, the charges will have to give up twice as much energy to get through the 10 Ohm resistor as they do to get through the 5 Ohm resistor. Consequently, one third of the charge's energy will be transferred to the 5 Ohm resistor and two-thirds to the 10 Ohm resistor. The loop rule is satisfied by 12 V across the battery = 4 V drop across the 5 Ohm resistor and an 8 Ohm drop across the 10 Ohm resistor.
In the parallel circuit, note that the voltage drop across each resistor is still equal to the battery voltage. In this case the current will not be the same in each branch, but the change in energy per charge is the same across each resistor.

Ohm's law: Resistance (in Ohms) = Voltage/Current
In the previous sections we have established that current is inversely proportional to resistance and current is directly proportional to voltage. Combining these relations we get current = voltage/ resistance. Solving for resistance: resistance = voltage/current. Solving for voltage, voltage = current x resistance, or V = IR.

Power is the amount of energy transferred each second: Power (in watts) = Voltage x Current

The actual brightness of the bulb depends not only on the number of charges flowing through the bulb each second (current), but also the energy per charge (voltage). The product of current and voltage is a rate of energy transfer, power.

Let us look at the energy transfer in series and parallel circuits.

In the series circuit, the current is the same through both resistors; however the voltage drop is not. Using Ohm’s law, we can determine that the current in the circuit is I = V/R = 12 V/15Ω = 0.8 A. So the energy transferred by the 5 Ohm resistor is 3.2 Watts and the energy transferred by the 10 Ohm resistor is 6.4 Watts. Note that if the resistors were light bulbs, the 10 Ohm resistor would correspond to the brighter bulb.
In the parallel circuit, the voltage is the same across each branch. The current flowing through the 5 Ohm branch is V/R = 2.4 A, more than the current flowing in the 10 Ohm branch, V/R = 1.2A. So the energy transferred by the 5 Ohm resistor is IV = 28.8 Watts and the energy transferred by the 10 Ohm resistor is IV = 14.4 Watts. Note that in this case, the 5 Ohm resistor would correspond to the brighter bulb.

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