| Resistors | |||
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Definition Value Identification Ohm's Law Voltage Dividers Voltage Divider Application Other Resistor Configurations Power Dissipation Definition: As the name implies, a resistor imposes a resistance (often called impedance) on current flow. I'm sure most people reading this will have, at some stage, encountered the dangers of excess current and the damage it can do to. Thus, the resistors most common use is to limit current to safe levels. Cheap insurance.... Value Identification: The value of a resistor is identified by a series of at least 4 colored bands. This because on components as small as 0.25W resistors a printed value would be very difficult to read and very easy to rub off. The code itself is quite simple; The first two bands represent the two (or three) most significant figures of the resistors value, the next band is the multiplier or number of zeros, and the last band is the tolerance. (how far off the stated value the part could actually be) The color code is given below.  This resistor is quite obviously 120KΩ. The gold and silver multipliers will make the value smaller. The color code "Brown-Green -Gold equals 15 x 0.1, or 1.5Ω. Tolerance is better described as accuracy. If you have a 1KΩ resistor with ±5% tolerance, you could have a resistor with a value anywhere between 950Ω and 1050Ω. (50Ω is 5% of 1000Ω) I've never seen a 10% tolerance resistor myself, and would probably decline to use it in most cases. If you can afford an extra 5c per piece, 1% tolerance resistors are a good rule of thumb. (in my opinion anyway) Occasionally you will find resistors marked in a different fashion. A resistor with a single black band is a "0Ω" resistor or an expensive wire link. Some high power resistors (over 1W) may have their value printed on them explicitly or in numeric IEC code which is the same as above but it uses numbers, not colors. This is quite rare. Ohm's Law: Below is something a surprising number of electronic enthusiasts do not understand, or use. Yes, it's Ohms Law again. Basic, but somewhat fundamental to electronics.... 
Using ohms law, we can quickly calculate the required resistance to obtain a specific maximum current at a certain voltage. Say you have an high intensity LED, one of those cool electric blue ones, and you want to get the best light show you can without toasting the LED. Somewhere on the complicated looking piece of paper often supplied with high performance LEDs will be a maximum forward current rating, usually along the lines of 40mA. To find the resistor needed, simply divide the supply voltage (which can be anything up to the LEDs breakdown voltage) by the maximum forward current. At 13.8V, (in a car) a 345Ω resistor is required. A good idea would be to take this up to the more readily available 390Ω rather than 330Ω. (which would result in more than 40mA) From ohms law again, we can find that 390Ω will allow 35.4mA to flow. Of course, ohms law is not limited to LEDs. It can be used in any situation where two of the three variables are known. As voltage is almost always known, I mostly use ohms law to determine resistor values. Voltage Dividers: Resistors can also be used to determine voltages, in a configuration called a voltage divider. 
The ratio of R1 to R2 determines VOUT, allowing any voltage within VIN to be obtained. Logically, if R1 and R2 are equal VOUT will be exactly half of VIN. Although the ratio between the two resistors is what determines the output, some thought should be given to actual values chosen. If you look at the circuit you will see that current must pass through R1 in order to reach VOUT, thus R1 determines the current available at VOUT. (use ohms law to determine this current) Because the desired ratio must be maintained to obtain the correct VOUT, reducing R1 to increase available current means we must also reduce R2. In the above circuit R1 and R2 will allow a certain amount of current to flow across VIN to no useful purpose. (ie. it is wasted) Furthermore, if the current flowing through the voltage divider is to large it will lower VOUT. (just like fast current flow in a water pipe results in low static pressure) In short, you cannot draw large amounts of current through a voltage divider and should usually use resistors greater than say, 10KΩ. When using a voltage divider in a noise sensitive application, such as an op-amp circuit then further thought should be given to the values used. Large values (such as 100KΩ, 1MΩ or even higher will draw very little current but are more susceptible to noise. Smaller values like 10KΩ, 1KΩ or less are better but will draw more current, which can quickly become a problem in itself. It's worth noting that any noise on VIN will appear proportionally in VOUT. This can be mitigated to some extent by decoupling VOUT. Voltage Divider Application: More interesting results can be achieved if one (or both) of the resistors and replaced with a variable resistor. The below circuit is a very basic light activated switch which makes use of variable resistors in voltage dividers. 
In bright light the LDR has a low resistance, (a few hundred ohms under a 100W bulb) placing a potential close to Vcc on the BC457's base, which is connected to "VOUT" of the voltage divider circuit. This will cause the BC547 to conduct, same with the BC337 which will pull in the relay. The 100Ω, 1KΩ and 10KΩ resistors are for current limiting. A power diode has been placed across the relay coil to protect the BC337 from high voltage spikes often generated by the relay coil when switching on or off, by shorting them to Vcc. (the diode will become forward-biased when a voltage 0.6V greater than Vcc appears at the collector of the BC337) The 10K potentiometer is a sensitivity adjust. The smaller resistance it presents between the BC547 and Vss the larger the amount of light required to turn the relay on. (use the voltage divider formula) If the BC547's base is pulled directly to ground by the pot the circuit cannot turn on. (again use the formula) Other Resister Configurations: Unfortunately, (but understandably) resistors are not available in any value we might happen to calculate, and those values which are available are often not close enough. In situations like these you have two options; use a trim-pot (a small adjustable resistor) or combine two or more resistors to get the required value. Trim-pots are too expensive to use for every case, but resistor combinations can cost as little as 15c but require some time with a calculator, rather than a precision screwdriver. Below is the two basic combinations of resistors, or any passive component for that matter. Series or parallel. These simple circuits can be combined in many ways to achieve the desired results. 
Calculating values for two or more resistors in series is simple, add all the values up. This is because all current must flow through all resistors, thus both resistances are imposed on the same potential. RTOTAL will always be greater than any of the included resistors. Parallel resistances are a little more complicated. When an electrical potential (voltage) encounters two possible paths, it will divide. If the two resistances are equal the current will divide equally and the RTOTAL will be exactly half of either resistor or exactly one third if their are three resistors. (and so on, there is no limit) This is because the current flow will split and be limited (as by ohms law above) by each resistor individually, and then added together. So, if 0.5A was able to flow through each resistor then 1A would flow in total. This is the same as using a single resistor with half the value. Now if two different resistors are used the current will still split, but not evenly. More current will take the path of least resistance and less current will take the path of higher resistance. The total current is still always less than would be for either resistor alone, and can be precisely calculated from the formula above. Just remember that the result is also a reciprocal and must be reciprocated to obtain the correct result. Power Dissipation: It is also worth noting that when two resistors are in parallel then their overall power rating (eg. 0.25W each) is increased. If both resistors are the same value and same power rating, then the total power rating is doubled. If parallel resistances are not equal, then the resistors with smaller values will be required to handle more power. This is most useful when you require higher power handling, but don't want to go out and buy more expensive (and physically larger) resistors. Four identical 0.25W resistors can be wired in parallel to give a resistor with one fourth the value in ohms, but four times the power rating. (1.0W) 
For the mathematically inclined, power (in watts) can be calculated by multiplying voltage by current. By using ohms law, the parallel or series resistor formulas and the above formula, a minimum power rating for a certain resistor can be calculated. If this is exceeded the resistor is likely to get hot and hopefully quietly breakdown. Just as likely, it could start a fire. So do your maths, it pays off in the end.... If you have any comments or questions please don't hesitate to contact me. |
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