Topic
• Circuits Tutorial
• Circuits I
• Electricity
The flow of electrons between adjacent atoms whose valence shells are not full. Materials that pass electrons freely are known as conductors. The most commonly used conductors are copper, tin, aluminum, silver, gold. Materials whose valence shell is full are said to be stable and are called insulators. Insulators do not absorb or release electrons and are used to isolate sections of conductive material from one another.
• Current, Voltage, Resistance
Current describes the quantity of electrons passing through a point in a circuit at a given instant in time.
Current is measured in Amperes (Amps, A).

Voltage describes the potential difference in electrical charge between two points in an electrical circuit. Voltage (also known as Electro motive force or EMF) is measures in Volts.

Resistance (a special case of Impedance) describes the capacity of a circuit element to resist or impede the flow of electrons in the circuit. Resistance in measure in Ohms ( symbol )

A common analogy may be used to relate these three quantities to water flow in pipes in place of electrons in wires. Current is analogous to the quantity of water flowing through a pipe at a given moment in time. Imagine you have two water tanks connected from the bottoms by a pipe (such as the drain of a double sink). If one tank is full of water and the other one empty we know intuitively that the water in the full tank will flow through the pipe into the empty tank until the level of water in the two tanks is equalized. The water in the full tank near the drain pipe is under pressure caused by gravity acting on the water above it in the tank. The difference in pressure between the water at the bottom of the full tank and the bottom of the empty (or only slightly full tank) is analogous to the voltage between poles of a battery (recall that voltage is always measured with respect to two distinct point in a circuit). In the case of a battery there is an excess of electrons present at the negative pole which are attracted to the electron holes at the positive pole with a potential or voltage determined by the chemical and physical properties of the battery.

Q: Would the voltage be different if we made the full tank taller and skinnier? no

Q: would the voltage change if we increased the amount of water in the full tank? yes - more water means more gravity acting on the water which results in greater pressure at the bottom of the tank.

Q: What happens if we open the pipe between the two tanks and let water flow? It flows from the full tank to the empty one until the level is the same in both. The same happens if you short the leads of a battery together without a resistor in between.

So what governs the time taken to equalize the level in the two tanks? The diameter of the pipe. The larger the pipe the less resistance there is to the water flow (or current) and the faster the levels equalize. Placing a resistor in an electric circuit has the same effect as placing a constriction in a water pipe. The amount of flow (or current) is not fixed, but given the same water pressure (or Voltage) the smaller the constriction the less flow occurs. Increasing the water pressure can counteract the reduction in flow. You can think of a battery as a pair of tanks, one full extra electrons and one empty to which extra electrons are attracted. (does adding constrictions hold in water as for electricity?) .... ohm's law ...

• Ohm's Law V = IR
Ohm's Law states that Voltage = Current x Resistance V = IR The equation can be rearranged to find any one of the three quantities given the other two. Consider the following circuit: ; The voltage in the circuit is given (10V from the battery) and the resistance is also given as the 100 ohm resistor is the only resistive element in the circuit. So we can compute the current in the circuit as: I = V/R = 10V / 100 Ohms = 0.1 Amps or 100 milli-Amps
• Watt's Law P = VI
Watt's Law states that: Power (in Watts) = Voltage (in Volts) x Current (in Amps) P = V I Combining with Ohm's law we get two other useful forms: P = V*V / R and P = I*I*R Power is a measurement of the amount of work that can be done with the circuit, such as turning a motor or lighiting a light bulb. Consider a 100Watt light bulb in your home. We know the voltage applied to the bulb is normally 110V or 220V so we can calculate the current consumed as follows: I = P/V = 100W / 110V = 0.91 Amps or I = P/V = 100W / 220V = 0.45 Amps So you can see why using a 60W light buld is more economical. Your electric company normally charges you for your usage in Killo-Watt Hours (kWh). One kWh is the amount of energy necessary to do 1000 Watts of energy for one hour - in other words to keep 10 100W light bulbs shining for one hour.
• Series Circuits
Consider this slightly more complicated circuit:

When two resistors are connected in series, their combined resistance is equivalent to the sum of their individual resistances.

We can use Ohm's law to calculate the voltage drop around each of the individual resistors after calculating the voltage drop accross the total resistance.
• Parallel Circuits
When two resistors are placed in parallel in a circuit their combined resistance is equal to the product of the individual resistances divided by their sum. (smaller total voltage for parallel in contrast to larger for series). One again we use ohm's law to calculate the voltage across the resistors (same for both) and the current through each resistor.
• Button / LED example
The following circuit diagram show the most basic LED (Light Emitting Diode) circuit.

Diodes are from the family of semiconductors. Unlike a resistors, diodes always have a fixed voltage drop in a circuit. A diode passes current in only one direction, a very useful property for protecting circuits from incorrect. The arrow in the diode symbol points in the direction that current flow, so normally you would place a diode in your circuit with the arrow pointing to ground. On the physical package of a diode the corresponding side is usually marked with a flat spot. As we will see later based on KCL we know the the current in a circuit is the same in each component of a branch. Therefore once we know the current passing through the resistor in this circuit we also know the current passing through the LED. The brightness of an LED is proportional to the amount of current passing through it. How would you make the LED shine brighter? less brightly?

Now consider the following circuit which adds a button:

The button simply interrupts or re-connects the flow of current through the circuit lighting or extinguishing the LED in the process.

• Power Sources
• Direct Current (DC)
A source that provides a constant voltage difference between it's leads (and thus a constant current) . Batteries, Many wall-wart style Power Supplies. Note that both of these sources have maximum current ratings and will only deliver stable contant voltage and current within that current rating. More on reading power supply ratings....
• Alternating Current (AC)
As found in all wall power supplies. Two leads, one cold lead acts as the 0V reference. The second or hot lead provides a sinusoidally oscillating voltage at a frequency and maximum voltage dependant on where you are!
• Circuits II
• KVL
Kirchkov's Voltage Law (KVL) states that .... voltage accross each branch in a circuit is equivalent.
• KCL
Kirchkov's Current Law (KCL) - states that the sum of the currents entering any node and those leaving that node in a circuit are equal.

KCL Reference
• Glossary
• Electron
• Electricity
• Resistor
• Resistance
• Ohm
• Ohm's Law
• Capacitor
• Capacitance
• Watt's Law
• Watts
• Power
• Energy
• Voltage
• Node
• Branch
• Inductor
• Inductance
• Henry
• Diode
• Transistor
• AC
• DC