Electricity is all around us, from the lighting in our houses to the computing in our personal computers.
These are powered by complex circuits.
The basics of simple direct current circuits will be studied in this chapter.
The standard convention of referring to a change in potential as a voltage is used in this chapter.
As you move forward, make a note of this so that you don't get confused.
Within the metal, electrons are travelling at a million m/s in random directions, colliding with other electrons and positive ion in the lattice.
Net movement of charge is not constituted by this because the electrons move randomly.
There is no current if there is no net motion of charge.
If we created a potential difference between the ends of the wire, the electrons would experience an electric force, and they would start to drift through the wire.
Although the electric field would travel through the wire at nearly the speed of light, the electrons themselves would still have to make their way through a crowd of atoms and other free electrons, so their drift speed would be relatively slow, on the order of a millimeter per second.
There is a flow of air in a particular direction when the wind blows.
The rate of motion of air molecule is being considered when talking about wind.
The rate of motion of electric charge is considered when talking about current.
To measure the current, we need to know how much charge crosses a plane per unit time.
Current is expressed in coulombs per second.
One coulomb per second is an Amp.
So 1 A is 1 C/s.
The direction of the current is taken to be the direction that positive charge carriers would move.
The current points toward the left if the electrons drift to the right.
Benjamin Franklin made an error when he first started investigating.
Current direction is in the flow of positive charges.
Let's say we had a copper wire and a glass fiber that had the same length and cross-sectional area, and that we connected the ends of the metal wire to the battery and measured the current.
The glass gave more resistance to the charge.
Resistance and Resistivity are not the same.
Resistance is the amount of resistance that prevents the passage of electric current.
A material's resistivity is determined by how the molecules that make it are bound together.
The units of resistivity are not the same.
The material and shape of the object affect its resistance.
Think of the copper wire and glass fiber in the same way.
Their resistances are different because they are made of different materials.
The resistivity of glass is much higher than that of copper.
Resistance depends on how the material is shaped, as well as on the material's characteristic resistivity.
This equation only applies to shapes with constant cross-sectional area, such as a cylinder or a rectangular prism, and will not apply to shapes with a different cross-sectional area.
Theresistivity is 1 x 10 -7 *m and the wire is made of Platinum.
The resistance of a wire depends on several factors.
These are wires, and they conduct electricity.
There are two types ofresistors, one of which is proportional to the voltage and the other of which is not.
Ohmic resistors are devices which obey Ohm's Law.
They will almost always be Ohmic, but you may be asked to qualitatively describe non-Ohmic wires.
A plot of the voltage versus the current can be used to determine whether or not a resistive element obeys the law.
A directly proportional graph will show that the wire is Ohmic, while a non-Ohmic plot will show that the resistor is non-Ohmic.
The graph will have a slope that is equal to the resistance of the wire.
The resistance is expressed in units of volts per Amp.
One watt is one watt.
1 V/A is 1
One answer is to say that there's an electric field inside the wire, and since negative charges move in the opposite direction to the electric field lines, electrons would drift opposite the electric field.
There are differences in air pressure that cause the wind to blow.
The wind won't blow if the air pressure is the same.
The source of current flow is similar to the pressure difference being the source of wind blowing.
The answer to the question is that there is a difference between the ends of the wire.
Negative charges move from higher potential to lower potential.
A conductor creates a current.
It is not uncommon to see the cause of the current that creates it, since it is the cause that sets the charges into motion.
A battery for direct current circuits is the source of the voltage in a circuit.
The potential difference is measured in J/C, not newtons.
An electric current is maintained when the terminals of a voltage source are connected by a conducting pathway.
If the current always travels in the same direction through the pathway, it's called a direct current.
In order to imagine what's happening in a circuit in which a steady-state current is maintained, let's follow one of the charge carriers.
The electric field pushes the charge into the wire from the positive terminal of the battery.
It encounters resistance, bumping into the relatively stationary atoms that make up the metal's lattice and setting them into greater motion.
The thermal energy of the wire comes from the electrical potential energy that was left in the battery.
All of the original electrical potential energy is lost when the charge reaches the negative terminal.
In order to keep the current going, the voltage source has to do positive work on the charge and move it from the negative terminal to the positive terminal.
The charge is ready to travel around the circuit again.
The power in a circuit is related to the heat given off.
The light bulb would become hot if we touched it.
The brighter the light bulb, the hotter it is.
The carrier of positive charge q loses potential energy when it drops by an amount.
If this happens in time, the rate at which this energy is transformed is equal to V.
This equation works for the power delivered by a battery to the circuit.
The dissipated power is given by the ratio of P to IV.
The power dissipated by the resistor is always P, regardless of whether or not it obeys the law.
When current passes through the resistors, they become hot.
A way of specifying the current, voltage, and power associated with each element in a circuit will be developed.
The circuits will contain batteries, resistors and connecting wires.
The resistance of an ordinary metal wire is negligible, and resistance is provided by devices that control the current: resistors.
The calculated value of R is relatively high compared to the other wires in the circuit because of the specific length, area, and resistivity of the Resistors.
The resistance and electric potential of the battery are shown.
Before the electrons return to the battery, all their energy is lost in the circuit.
Since the only thing in this circuit that requires energy for charge to move through is the Resistor, no energy is used to move from one side of the wire to the other.
It's easy to determine the current in this case.
The effect of two resistors can be equaled by one.
To simplify the circuit, you need to find the equivalent resistance of combinations.
Any two resistors can be treated as a single equivalent.
The way the resistors are arranged can affect the way you combine them.
A pair of resistors can be arranged in different ways.
In a series branch, the current is the same through each resistor, and the voltage drop is the same.
If they are arranged one after the next, they are in a series.
In such an arrangement, the current that flows into the first resistor must flow into the second.
The new wire would need to be longer to match the arrangement.
The resistance of the resistors is larger when they are arranged in a series.
If the total voltage drop across them is equal to the sum of the individual voltage drops across each Resistors are said to be in series if they all share the same current and if the total voltage drop across them is equal to the sum of the individual voltage drops across each
It makes sense that in a set of parallel resistors, a larger amount of current will want to travel through the path of least resistance, if two of them are in parallel.
A mistake happens when calculating an equivalent for a set of parallel resistors.
Write the equation down.
The final step in calculating the equivalent resistance is taken by students.
If the current that flows through one of the resistors can't go through the other, there is a junction before the other.
Since the charges are spread out along either of two paths, the new wire would need to have a larger area to match this arrangement.
The equivalent resistance is smaller when the resistors are arranged in parallel.
There is a split of the total current entering the combination.
Imagine that I enter the combination.
Some of the current would go through R 1 and the rest would go through R 2.
The voltage is the same for each Resistor and they are in parallel.
The idea of resistors in series can be applied to any number of them.
The following three resistors have the same resistance.
The ide of parallel resistors can be applied to any number of resistors that are arranged in parallel.
The following three resistors have the same resistance.
When a circuit has more than two resistors, it is1-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-6556 It is1-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-6556 When this is the case, the equivalent resistance of the part of the circuit that is parallel must be found first, and then used for further calculations.
The three resistors are not in parallel or in series.
There must be a pair that is not in a straight line.
The 3 O or 6 O resistors are not parallel to the 4 O one.
Because of the junction before that combination, the 3 O and 6 O can't carry the current that flows through the 3 O.
The current that flows into the 4 O must flow into this equivalent resistors, so this resistance is in a series.
R is the total resistance in the circuit.
The easiest problem to solve is the oneresistor problem.
You can use Ohm's Law to solve for the current that flows out of the battery into the circuit if you represent many combinations of resistors in series or parallel.
A simple circuit with a battery and an equivalent is the most common method of working a circuit problem.
We build the circuit back to its original form after we solve for individual values on each Resistor.
The circuit was simpler in the diagram to the right.
We work backwards from 3 to 2 to 1 to solve the problem.
Each time we replace a combination of resistors, you might want to change the circuit.
We can return to the original circuit.
The current is 2 A and we have to return to the diagram.
The diagram shows the current through the resistors.
Since we know the current through the resistors, we can use the equation V + IR to figure out the voltage drop.
The total voltage drop across the two resistors is 12 V, which matches the drop across the 4 resistors.
Going from diagram to diagram is the last step.
There is nothing that needs to be done with the 4resistor and the 2resistor in the diagram goes back to the parallel combination.
The voltage drop is back to the diagram.
The two parallel resistors in the diagram have a 4 V drop across them.
We can figure out the current through the resistors by using the equation I = V / R. The current through the 3 and 6 are equal to A.
The total current passing through the individual resistors is equal to the current entering the parallel combination.
We will calculate the dissipated power by the heat of the resistors.
We can use any of the equivalent formulas.
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