Basic Appliance Theory

August 9, 2009

What is inside an appliance?
There isn’t much rocket science in the typical small appliance (though that is changing to some extent with the use of microcomputer and fuzzy logic control). Everything represents variations on a relatively small number of basic themes:

  • Heating – a resistance element similar to what you can see inside a toaster provides heat to air, liquids, or solids by convections, conduction, or direct radiant (IR) heat.

  • Rotation, blowing, sucking – a motor provides power to move air as in a fan or vacuum cleaner, water as in a sump pump, or provide drive as in an electric pencil sharpener, food mixer, or floor polisher.

  • Control – switches and selectors, thermostats and speed regulators, and microcomputers determine what happens, when, how much, and assure safe operation.

Basic electrical principle
Relax! This is not going to be a tutorial on computer design. Appliances are simple devices. It is possible to repair many appliance faults without any knowledge beyond ‘a broken wire is probably a problem’ or ‘this part is probably bad because it is charred and broken in half’. However, a very basic understanding of electrical principles will enable you to more fully understand what you are doing. Don’t worry, there will be no heavy math. The most complicated equations will be variations on Ohm’s law: V=I*R and P=V*V/R.

Voltage, current, and resistance
If you have any sort of background in electricity or electronics, then you can probably skip the following introductory description – or have some laughs at my expense.

The easiest way to explain basic electrical theory without serious math is with a hydraulic analogy. This is of the plumbing system in your house:

Water is supplied by a pipe in the street from the municipal water company or by a ground water pump. The water has a certain pressure trying to push it through your pipes. With electric circuits, voltage is the analog to pressure. Current is analogous to flow rate. Resistance is analogous the difficulty in overcoming narrow or obstructed pipes or partially open valves.

Intuitively, then, the higher the voltage (pressure), the higher the current (flow rate). Increase the resistance (partially close a valve or use a narrower pipe) and for a fixed voltage (constant pressure), the current (flow rate) will decrease.

With electricity, this relationship is what is known as linear: double the voltage and all other factors remaining unchanged, the current will double as well. Increase it by a factor of 3 and the current will triple. Halve the resistance and for a constant voltage source, the current will double. (For you who are hydraulic engineers, this is not quite true with plumbing as turbulent flow sets in, but this is just an analogy, so bear with me.)

Note: for the following 4 items whether the source is Direct Current (DC) such as a battery or Alternating Current (AC) from a wall outlet does not matter. The differences between DC and AC will be explained later.

The simplest electrical circuit will consist of several electrical components in series – the current must flow through all of them to flow through any of them. Think of a string of Christmas lights – if one burns out, they all go out because the electricity cannot pass through the broken filament in the burned out bulb.

Note the term ‘circuit’. A circuit is a complete loop. In order for electricity to flow, a complete circuit is needed.

                          Switch (3)
               _____________/ ______________
              |                             |
              | (1)                         | (4)
      +-------+--------+                +---+----+
      |  Power Source  |                |  Load  |
      +-------+--------+                +---+----+
              |            Wiring (2)       |
              |_____________________________|

  1. Power source – a battery, generator, or wall outlet. The hydraulic equivalent is a pump or dam (which is like a storage battery). The water supply pipe in the street is actually only ‘wiring’ (analogous to the electric company’s distribution system) from the water company’s reservoir and pumps.

  2. Conductors – the wiring. Similar to pipes and aqueducts. Electricity flows easily in good conductors like copper and aluminum. These are like the insides of pipes. To prevent electricity from escaping, an insulator like plastic or rubber is used to cover the wires. Air is a pretty good insulator and is used with high power wiring such as the power company’s high voltage lines but plastic and rubber are much more convenient as they allow wires to be bundled closely together.

  3. Switch – turns current on or off. These are similar to valves which do not have intermediate positions, just on and off. A switch is not actually required in a basic circuit but will almost always be present.

  4. Load – a light bulb, resistance heater, motor, solenoid, etc. In true hydraulic systems such as used to control the flight surfaces of an aircraft, there are hydraulic motors and actuators, for example.

    With household water we usually don’t think of the load. However, things like lawn sprinklers, dishwasher rotating arms, pool sweepers, and the like do convert water flow to mechanical work in the home (some homes, at least!). Hydraulic motors are used to aircraft and spacecraft, large industrial robots, and all sorts of other applications.

Here are 3 of the simplest appliances:

  • Flashlight: battery (1), case and wiring (2), switch (3), light bulb (4).

  • Table lamp: wall outlet (1), line cord and internal wiring (2), power switch (3), light bulb (4).

  • Electric fan, vacuum cleaner, garbage disposer: wall outlet (1), line cord and internal wiring (2), power switch (3), motor (4).

Now we can add one type of simple control device:

  1. Thermostat – a switch that is sensitive to temperature. This is like an automatic water valve which shuts off if a set temperature is exceeded. Most thermostats are designed to open the circuit when a fixed or variable temperature is exceeded. However, air conditioners, refrigerators, and freezers do the opposite – the thermostat switches on when the temperature goes too high. Some are there only to protect against a failure elsewhere due to a bad part or improper use that would allow the temperature to go too high and start a fire. Others are adjustable by the user and provide the ability to control the temperature of the appliance.

With the addition of a thermostat, many more appliances can be constructed including (this is a small subset):

  • Electric space heater (radiant), broiler, waffle iron: wall outlet (1), line cord and internal wiring (2), power switch (3) and/or thermostat (5), load (heavy duty heating element).

  • Electric heater (convection), hair dryer: wall outlet (1), line cord and internal wiring (2), power switch (3) and/or thermostat (5), loads (4) (heating element and motor).

Electric heaters and cooking appliances usually have adjustable thermostats.

Hair dryers may simply have several settings which adjust heater power and fan speed (we will get into how later). The thermostat may be fixed and to protect against excessive temperatures only.

That’s it! You now understand the basic operating principle of nearly all small appliances. Most are simply variations (though some may be quite complex) on these basic themes. Everything else is just details.

For example, a blender with 38 speeds just has a set of buttons (switches) to select various combinations of motor windings and other parts to give you complete control (as if you need 38 speeds!). Toasters have a timer or thermostat activate a solenoid (electromagnet) to pop your bread at (hopefully) the right time.

  1. Resistances – both unavoidable and functional. Except for superconductors, all materials have resistance. Metals like copper, aluminum, silver, and gold have low resistance – they are good conductors. Many other metals like iron or steel are fair but not quite as good as these four. One, NiChrome – an alloy of nickel and chromium – is used for heating elements because it does not deteriorate (oxidize) in air even at relatively high temperatures.

    A significant amount of the power the electric company produces is lost to heating of the transmission lines due to resistance and heating.

    However, in an electric heater, this is put to good use. In a flashlight or table lamp, the resistance inside the light bulb gets so hot that it provides a useful amount of light.

    A bad connection or overloaded extension cord, on the other hand, may become excessively hot and start a fire.

The following is more advanced – save for later if you like.

  1. Capacitors – energy storage devices. These are like water storage tanks (and similar is some ways to rechargeable batteries). Or, a system consisting of a a rubber diaphragm separating the water from a volume of trapped air. As water is pumped in, energy is stored as the air is compressed as in the captive air or expansion tanks found in home heating systems or well water storage tanks.

    Capacitors are not that common in small appliances but may be used with some types of motors and in RFI – Radio Frequency Interference – filters as capacitors can buffer – bypass – interference to ground. The energy to power an electronic flash unit is stored in a capacitor, for example. Because they act like reservoirs – buffers – capacitors are found in the power supplies of most electronic equipment to smooth out the various DC voltages required for each device.

  2. Inductors – their actual behavior is like the mass of water as it flows. Turn off a water faucet suddenly and you are likely to hear the pipes banging or vibrating. This is due to the inertia of the water – it tends to want to keep moving. Electricity doesn’t have inertia but when wires are wound into tight coils, the magnetic field generated by electric current is concentrated and tends to result in a similar effect. Current tends to want to continue to flow where inductance is present. (For the more technical reader, the air chamber used to prevent/minimize the water hammer effect is the equivalent of an RC snubber!)

    The windings of motors and transformers have significant inductance but the use of additional inductance devices is rare in home appliances except for RFI – since inductance tends to prevent current from changing, it can also be used to prevent interference from getting in or out.

  3. Controls – rheostats and potentiometers allow variable control of current or voltage. A water faucet is like a variable resistor which can be varied from near 0 ohms (when on fully) to infinite ohms (when off).

Ohm’s Law
The relationships that govern the flow of current in basic circuits (without capacitance or inductance – which is the case with many appliances) are contained in a very simple set of equations known an Ohm’s Law.

The simplest of these are:

                    V = I * R (1)<br />                    I = V / R (2) <br />                    R = V / I (3)<br />

Where:

  • V is Voltage in Volts (or millivolts – mV or kilovolts – kV).
  • I is current in amperes (A) or milliamps (mA)
  • R is resistance in Ohms (ohms), kilo-Ohms (K Ohms), or mega-Ohms (M Ohms).

Power in watts (W) is equal to voltage times current in a resistive circuit (no capacitance or inductance). Therefore, rearranging the equations above, we also obtain:

                    P = V * I      (4)<br />                    P = V * V / R  (5)<br />                    P = I * I * R  (6)<br />

For example:

  • For a flashlight with a pair of Alkaline batteries (3 V) and a light bulb with a resistance of 10 ohms, we can use (2) to find that the current is I = (3 V) / (10 ohms) = .3 A. The from (4) we find that the power is: P = (3 V * .3 A) = .9 W.

  • For a blow-dryer rated at 1000 W, the current drawn from a 120 V line would be: I = P / V (by rearranging (4) = 1000 W / 120 V = 8.33 A.

As noted above:

  • Increase voltage -> higher current. (If the water company increases the pressure, your shower used more water in a given time.)

  • Decrease resistance -> higher current. (You have a new wider pipe installed between the street and your house. Or, you open the shower valve wider.)

(Note that the common use of the term ‘water pressure’ is actually not correct. The most likely cause of what is normally described as low water pressure is actually high resistance in the piping between your residence and the street. There is a pressure drop in this piping just as there would be a voltage drop across a high value resistor.)

DC and AC
While electricity can vary in any way imaginable, the most common forms for providing power are direct current and alternating current:

A direct current source is at a constant voltage. Displaying the voltage versus time plot for such a source would show a flat line at a constant level. Some examples:

  • Alkaline AA battery – 1.5 V (when new).
  • Automotive battery – 12 V (fully charged).
  • Camcorder battery – 7.2 V (charged).
  • Discman AC adapter – 9 VDC (fully loaded).
  • Electric knife AC adapter – 3.6 VDC.

An Alternating Current (AC) source provides a voltage that is varying periodically usually at 60 Hz (U.S.) or 50 Hz (many other countries). Note that 1 Hz = 1 cycle per second. Therefore, a 60 Hz AC voltage goes through 60 complete cycles in each second. For power, the shape of the voltage is a sinusoid which is the smoothest way that anything can vary periodically between two levels.

The nominal voltage from an AC outlet in the U.S. is around 115 VAC. This is the RMS (Root Mean Square) value, not the peak (0 to maximum). In simple terms, the RMS value of an AC voltage and the same value of a DC voltage will result in identical heating (power) to a resistive load. For example, 115 VAC RMS will result in the same heat output of a broiler as 115 VDC.

Direct current is used for many small motor driven appliances particularly when battery power is an option since changing DC into AC requires some additional circuitry. All electronic equipment require various DC voltages for their operation. Even when plugged into an AC outlet, the first thing that is done internally (or in the AC adapter in many cases) is to convert the AC to various DC voltages.

The beauty of AC is that a very simple device – a transformer – can convert one voltage into another. This is essential to long distance power distribution where a high voltage and low current is desirable to minimize power loss (since it depends on the current). You can see transformers atop the power poles in your neighborhood reducing the 2,000 VAC or so from a local distribution transformer to your 115 VAC (actually, 115-0-115 were the total will be used by large appliances like electric ranges and clothes dryers). That 2,000 VAC was stepped down by a larger transformer from around 12,000 VAC provided by the local substation. This, in turn, was stepped down from the 230,000 VAC or more used for long distance electricity transmission. Some long distance lines are over 1,000,000 volts (MV).

When converting between one voltage and another with a transformer, the amount of current (amps) changes in the inverse ratio. So, using 230 kV for long distance power transmission results in far fewer heating losses as the current flow is reduced by a factor of 2,000 over what it would be if the voltage was only 115 V, for example. Recall that power loss from P=I*I*R is proportional to the square of the current and thus in this example is reduced by a factor of 4,000,000!

Many small appliances include power transformers to reduce the 115 VAC to various lower voltages used by motors or or electrical components. Common AC adapters – often simply called transformers or wall warts – include a small transformer as well. Where their output is AC, this is the only internal component other than a fuse or thermal fuse for protection. Where their output is DC, additional components convert the low voltage AC from the transformer to DC and a capacitor smoothes it out.

Series and parallel circuits
Up until now, we have been dealing with the series circuit – all parts are in a single line from power source, wiring, switches, load, and anything else. In a series circuit, the current must be the same through all components. The light bulb and switch in a flashlight pass exactly the same value of amperes. If there were two light bulbs instead of one and they were connected in series – as in a Christmas tree light set – then the current must be equal in all the bulbs but the voltages across each one would be reduced.

The loads, say resistance heating elements, are now drawn with the schematic symbol (as best as can be done using ASCII) for a resistor.

                          Switch<br />               _____________/ __________________<br />              |                 I -->           |<br />              |                        ^    ^   |<br />              |                        |    |   / R1<br />              |                        |   V1   \ Load 1<br />      +-------+--------+               |    |   /<br />      |  Power Source  |                    v__ |<br />      +-------+--------+              V(S)  ^   |<br />              |                             |   / R2<br />              |                        |   V2   \ Load 2<br />              |                        |    |   /<br />              |                        v    v   |<br />              |_________________________________|<br /><br />

The total resistance, R(T), of the resistors in this series circuit is:

                    R(T) = R1 + R2                (7)<br />

The voltage across each of the resistors would be given by:

                    V1 = V(S) * R1 / (R1 + R2)    (8)<br />                    V2 = V(S) * R2 / (R1 + R2)    (9)<br />

The current is given by:

                    I = V(S)  / (R1 + R2)        (10)<br />

However, another basic configuration, is also possible. With a parallel circuit, components are connected not one after the other but next to one another as shown below:

                          Switch<br />               _____________/ ___________________________<br />              |                      I -->  |            |<br />              |                 ^           |            |<br />      +-------+--------+        |           / R1         / R2<br />      |  Power Source  |       V(S)         \ Load 1     \ Load 2<br />      +-------+--------+        |           /            /<br />              |                 v           |v I(1)      |v I(2)<br />              |_____________________________|____________|<br /><br />

Now, the voltages across each of the loads is necessarily equal but the individual currents divide according to the relative resistances of each load.

The total resistance, R(T), of the parallel resistors in this circuit is:

                    R(T) = (R1 * R2) / (R1 + R2)  (11)<br />

The currents through each of the loads would be given by:

                    I1 = V(S)/R1                  (12)<br />                    I2 = V(S)/R2                  (13)<br />

The total current is given by:

                    I = I1 + I2                   (14)<br />

Many variations on these basic arrangements are possible but nearly all can be reduced systematically to a combination of series or parallel circuits.

http://repairfaq.ece.drexel.edu/sam/appfaq.htm#afbatheory

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