## Free Study Material

What is Electricity
What is Current
What are Electric Potential and Voltage?
What Makes Current Flow Through a Circuit?
What are Batteries?
What are Resistors?
What are Wires?
What are Capacitors?
What are Inductors?
What is Kirchhoff's Current Law (KCL)?
What is Kirchhoff's Voltage Law (KVL)?
What are Current Sources?
How to Use a Voltmeter
How to Use an Ammeter (Current Meter)
How to Use Ohmmeters (Resistance Meters), Capacitance Meters, and Inductance Meters
How to Use Current Integrators
How to Use Voltage Integrators
SI Prefixes What is Electricity
Around every atom are microscopic indivisible particles called electrons. Electricity is the movement of electrons through conductors, such as metals, which allow electron movement. Electrons have a property called charge that makes them respond to electrical forces. Charge is analogous to mass, in that mass makes an object respond to gravitational forces, and charge makes an object respond to electrical forces. A mass can have gravitational potential energy, and a charge can have electrical potential energy. The analogy is not perfect, because charge can be positive or negative, and electrical forces are much stronger than gravitational forces. Charge is measured in coulombs, just as mass is measured in kilograms. The symbol for charge is a capital Q. The charge of one electron is designated as -1.602176487*10-19 coulomb.

What is Current
Current is the rate at which charge moves through a circuit. Current is measured in coulombs per second, or amps, and represented by a capital I. One amp corresponds to one coulomb passing by per second. Electrons have a negative charge, so when you say which way current flows, the electrons are actually moving in the opposite direction. You act as if electricity is the movement of positively charged particles. The direction confusion exists partly because electricity was discovered before electrons were discovered and it was known which way they move in a circuit.

What are Electric Potential and Voltage?
Electric potential is the amount of electric potential energy (EPE) stored per unit charge, and is measured in volts, or joules per coulomb. Electric potential is analogous to gravitational potential, the gravitational potential energy(GPE) stored per unit mass, which is measured in joules per kilogram. While potential energy is something that an object has, potential is a property of a location. Rather than discuss electric potential, it is more common to discuss voltage, which is the difference in electric potential between two points. An object at the top of a hill has more GPE than the same object at the bottom of the hill. This means that that the gravitational potential is greater at the top of the hill than at the bottom of the hill. Similarly, charge at the positive terminal of a battery has more electric potential energy than the same charge at the negative terminal. If a battery's voltage is 9 volts, it means that the electric potential at the positive terminal is 9 volts more than the electric potential at the negative terminal. Both electric potential and voltage are measured in volts and represented by a capital V. Voltage may also be represented as ΔV, which emphasizes the fact that it is a potential difference.

What Makes Current Flow Through a Circuit?
Electric charge moves under the influence of electrical forces. The electrical force is always in the direction of decreasing electric potential energy. This is analogous to the gravitational force which is in the direction of decreasing gravitational potential energy (down). The path that charge takes through a circuit is analogous to the path a skier takes through a skiing slope. The skier moves toward lower gravitational potential, losing GPE and producing heat, and then rides the lift, which expends energy to move the skier back to the top of the slope. In a circuit, charge moves toward lower electrical potential, losing EPE and producing heat. The battery expends energy to move the charge entering the battery through the negative terminal through the battery back to the positive terminal. It is common to see the terms voltage drop and voltage difference used instead of potential drop and potential difference.

What are Batteries?
A battery can be thought of as a pump for electrons that converts chemical energy in the battery into EPE. A battery is defined by the potential difference between its terminals, which is often represented by the symbol ℰ, making the battery obey the equation V = ℰ. Inside a battery, chemical reactions occur that cause electrons to be released from the negative terminal to the rest of the circuit and absorbed by the positive terminal from the rest of the circuit. Depending on the load attached to the battery, varying amounts of current will flow through the it. Don't short out a battery. Large amounts of current will flow through the circuit, which can cause excessive heat, fire, and explosion.

What are Resistors?
Resistors are components that dissipate EPE as heat. The voltage drop across a resistor is proportional to the current through it and described by Ohm's law, V = I * R, where R is the resistance of the resistor, measured in ohms (Ω), or volts per amp. The resistance tells how much voltage must be put across the resistor to obtain one amp of current. The larger the resistance, the more voltage it takes to move a current through the resistor. As the resistance approaches infinity, the resistor acts more like an open circuit, and as the resistance approaches zero, the resistor acts more like an ideal wire. With the exception of superconductors, all components in the real world have some amount of resistance.

What are Wires?
Wires are conductors that charge can move through with a negligible loss of EPE. Real wires have a small resistance, but when studying a model of a circuit, it is assumed that wires have zero resistance. The voltage difference across a wire is zero volts, represented as V = 0. The current through a wire depends on what it is connected to.

What are Capacitors?
Capacitors are components that store EPE in charged plates. Charge does not technically move through a capacitor. Charge enters one terminal of the capacitor where it sits on the first of the two plates, making the plate positively charged. At the same time, charge leaves the other terminal of the capacitor, coming from the second plate, leaving that plate negatively charged. It takes EPE to charge the capacitor, and when the capacitor discharges, EPE is released. The amount of charge on each plate is called the charge in or on the capacitor. When a capacitor holds no charge, it has no voltage across it. As a capacitor charges, its voltage increases. The charge in a capacitor and its voltage obey the law Q = C * V, where Q is the charge in the capacitor, and C is the capacitance of the capacitor, measured in farads, or coulombs per volt. The capacitance tells how much charge the capacitor will have when one volt is applied to it. If a capacitor is not connected to any other components (an open circuit), it will hold its charge, and if a capacitor is shorted out, it will discharge.

What are Inductors?
Inductors, like capacitors, are components that store and release energy. Inductors, however, store magnetic energy, which is converted to and from EPE. Physically, an inductor is a coil of wire. A current passing through an inductor produces a magnetic field which acts to maintain the current present in the inductor. When a voltage is applied across an inductor, the current will change at some rate. It takes energy to get a current to flow through an inductor, and energy is released when this current stops flowing. Inductors are described by the equation V = L * I′, where L is the inductance of the inductor, measured in henries, or volt seconds per amp, and I&prime is the rate that the current is changing, in amps per second. Inductance tells how much voltage must be placed across the inductor to make the current change at a rate of one amp per second. If an inductor is disconnected from all other components (an open circuit), current will not be able to flow through it and it will lose its stored energy. If an inductor is shorted out, placing zero volts across it, the current present will be maintained by the magnetic field.

What is Kirchhoff's Current Law (KCL)?
Kirchhoff's current law states that at any node in a circuit where components are connected together, the current entering that point must perfectly balance the current leaving. This is written as Iin = Iout. Kirchhoff's current law ensures that charge does not build up somewhere in the circuit- whatever charge enters a point must equal the charge that leaves that point. Kirchhoff's current law can also be considered a statement of the conservation of charge-charge cannot be created nor destroyed. Charge never enters nor leaves a circuit- it can only move from one place in a circuit to another.

What is Kirchhoff's Voltage Law (KVL)?
Kirchhoff's voltage law states that if you go around any loop in a circuit, the sum of the voltage differences across the components in the loop must add to zero. In other words, you must end up back at the same electric potential you started at. Kirchoff's voltage law is equivalent to stating that every point in a circuit has a single value for its electric potential and can be considered a statement of the conservation of energy. If charge could go around a loop in a circuit and end up at a higher potential than it started, it would be possible to make a perpetual motion machine.

What are Current Sources?
Current sources are components that have a constant amount of current through them. They will have whatever voltage across them that is needed to maintain this current. Similar to how a battery cannot be shorted out, a current source cannot be connected to an open circuit, because then the current is not able to flow. There must be a path for current to enter and leave the current source.

How to Use a Voltmeter
A voltmeter is used to measure the voltage difference between two points without affecting the circuit. To measure the voltage across a component, place a voltmeter in parallel with the component. A voltmeter has a very large resistance so that only a negligible amount of current is diverted from the circuit being analyzed. Physical voltmeters often have a resistance of 10MΩ, but the voltmeters in CircuitEngine have infinite resistance so that they draw zero current from the circuit. If you want the effect of a voltmeter with non-infinite resistance, you can place a large resistor in parallel with the voltmeter. The value displayed on the voltmeter is the amount that the voltage of the positive terminal (marked with a plus sign, with a red wire in physical voltmeters) is above the voltage of the negative terminal. If the voltmeter displays 1 volt, it means the positive terminal is one volt higher than the negative terminal. If the voltmeter displays negative 1 volt, it means that the positive terminal is one volt below the negative terminal. A voltmeter that is shorted out will display 0 volts, and a voltmeter that is not connected to other components (an open circuit) will not be able to determine the voltage difference.

How to Use an Ammeter (Current Meter)
An ammeter is used to measure the current that passes through a component and is placed in series with the component. An ammeter has a very small resistance so that only a negligible amount of voltage drop occurs across it. The ammeters in CircuitEngine have zero voltage drop across them so that they act like wires. If you want the effect of an ammeter with nonzero resistance, you can place a small resistor in series with the ammeter. The value displayed on the ammeter is the amount of current that flows through the ammeter from the positive terminal (marked with a plus sign, with a red wire in physical ammeters) to the negative terminal. If the ammeter displays one amp, it means that one amp of current is flowing from the positive terminal to the negative terminal inside the ammeter. If the ammeter displays negative one amp, it means that one amp of current is flowing from the negative terminal to the positive terminal inside the ammeter. An ammeter that is not connected to other components (an open circuit) will display 0 amps, and an ammeter that is shorted out will not be able to determine the current.

How to Use Ohmmeters (Resistance Meters), Capacitance Meters, and Inductance Meters
Ohmmeters, capacitance meters, and inductance meters can be used to measure the equivalent resistance, capacitance, and inductance of complex series and parallel combinations of resistors, capacitors, and inductors, respectively. Ohmmeters, capacitance meters, and inductance meters are active components, meaning that they generate EPE and should be removed from a circuit after a measurement is made. Ohmmeters can put a known amount of current through a resistor and measure the voltage drop across the resistor to determine the resistance. Capacitance meters can charge a capacitor with a known amount of current and measure the rate that the voltage changes to determine the capacitance. Inductance meters can place a known voltage across an inductor and measure the rate that the current changes to determine the inductance. To use one of these types of meters, make sure that the components that you are measuring are not connected to another circuit. For example, if you want to measure the resistance of a combination of resistors that is being used in a circuit, first disconnect the resistors from the rest of the circuit- you do not want to measure the rest of the circuit along with the resistors. Use these meters in CircuitEngine to measure what they are designed for- if you use them with the wrong types of component, you will get unexpected behavior.

How to Use Current Integrators
A current integrator is a meter that measures how much charge (in coulombs) has flowed through it from the positive terminal to the negative terminal. If you place a current integrator in series with a capacitor before charging it, as shown on the home page, you can measure the charge stored in the capacitor.

How to Use Voltage Integrators
A voltage integrator is a meter that measures how much magnetic flux (in webers or volt seconds) has formed between the positive terminal and the negative terminal. If you place a current integrator in parallel with an inductor before charging it, as shown on the home page, you can measure the magnetic flux through the inductor.

SI Prefixes
All of the SI prefixes used in CircuitEngine are described on Wikepedia. Note that an attoamp is approximately equivalent to six electrons per second.

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© 2009 Kevin Stueve kstueve@uw.edu. Web template by Andreas Viklund. 