Nov 29, 2008

RESISTORS and RESISTANCE

What do resistors do?

Resistors limit current. In a typical application, a resistor is connected in series with an LED:

resistors limit currentLEDs need a series resistor

Enough current flows to make the LED light up, but not so much that the LED is damaged. Later in this Chapter, you will find out how to calculate a suitable value for this resistor. (LEDs are described in detail in Chapter 5.)

The 'box' symbol for a fixed resistor is popular in the UK and Europe. A 'zig-zag' symbol is used in America and Japan:

resistor symbols

Resistors are used with transducers to make sensor subsystems. Transducers are electronic components which convert energy from one form into another, where one of the forms of energy is electrical. A light dependent resistor, or LDR, is an example of an input transducer. Changes in the brightness of the light shining onto the surface of the LDR result in changes in its resistance. As will be explained later, an input transducer is most often connected along with a resistor to to make a circuit called a potential divider. In this case, the output of the potential divider will be a voltage signal which reflects changes in illumination.

Microphones and switches are input transducers. Output transducers include loudspeakers, filament lamps and LEDs. Can you think of other examples of transducers of each type?

In other circuits, resistors are used to direct current flow to particular parts of the circuit, or may be used to determine the voltage gain of an amplifier. Resistors are used with capacitors (Chapter 4) to introduce time delays.

Most electronic circuits require resistors to make them work properly and it is obviously important to find out something about the different types of resistor available, and to be able to choose the correct resistor value, in , , or M, for a particular application.

 

 

Fixed value resistors

The diagram shows the construction of a carbon film resistor:

During manufacture, a thin film of carbon is deposited onto a small ceramic rod. The resistive coating is spiralled away in an automatic machine until the resistance between the two ends of the rod is as close as possible to the correct value. Metal leads and end caps are added, the resistor is covered with an insulating coating and finally painted with coloured bands to indicate the resistor value.

Carbon film resistors are cheap and easily available, with values within ±10% or ±5% of their marked, or 'nominal' value. Metal film and metal oxide resistors are made in a similar way, but can be made more accurately to within ±2% or ±1% of their nominal value. There are some differences in performance between these resistor types, but none which affect their use in simple circuits.

Wirewound resistors are made by winding thin wire onto a ceramic rod. They can be made extremely accurately for use in multimeters, oscilloscopes and other measuring equipment. Some types of wirewound resistors can pass large currents wihtout overheating and are used in power supplies and other high current circuits.

 

 

Current limiting

You are now ready to calculate a value for the resistor used in series with an LED. Look at the circuit diagram:

A typical LED requires a current of 10 mA and has a voltage of 2 V across it when it is working. The power supply for the circuit is 9 V. What is the voltage across resistor R1? The answer is 9-2=7 V. (The voltages across components in series must add up to the power supply voltage.)

You now have two bits of information about R1: the current flowing is 10 mA, and the voltage across R1 is 7 V. To calculate the resistance value, use the formula:

Substitute values for V and I:

Look out! The formula works with the fundamental units of resistance, voltage and current, that is, ohms, volts and amps. In this case, 10 mA had to be converted into amps, 0.01 A, before substitution.

If a value for current in mA is substituted, the resistance value is given in :

The calculated value for R1 is 700 . What are the nearest E12/E24 values? Resistors of 680 , 750 and 820 are available. 680 is the obvious choice. This would allow a current slightly greater than 10 mA to flow. Most LEDs are undamaged by currents of up to 20 mA, so this is fine. What is the colour code for a 680 resistor?

 

Power rating

When current flows through a resistance, electrical energy is converted into heat. This is obvious in an electric torch where the lamp filament heats up and glows white hot. Although the result may be less evident or imperceptible, exactly the same process of energy conversion goes on when current flows through any electronic component.

The power output of a lamp, resistor, or other component, is defined as the rate of change of electrical energy to heat, light, or some other form of energy. Power is measured in watts, W, or milliwatts, mW, and can be calculated from:

where P is power.

What is the power output of a resistor when the voltage across it is 6 V, and the current flowing through it is 100 mA?

0.6 W of heat are generated in this resistor. To prevent overheating, it must be possible for heat to be lost, or dissipated, to the surroundings at the same rate.

A resistor's ability to lose heat depends to a large extent upon its surface area. A small resistor with a limited surface area cannot dissipate (=lose) heat quickly and is likely to overheat if large currents are passed. Larger resistors dissipate heat more effectively.

Look at the diagram below which shows resistors of different sizes:

which resistor can take the biggest current without overheating?

The standard size of carbon film resistor used in most circuits has a power rating of 0.5 W. This means that a resistor of this size can lose heat at a maximum rate of 0.5 W. In the example above, the calculated rate of heat loss was 0.6 W, so that a resistor with a higher power rating, 1 W or 2 W, would be needed. Some resistors are designed to pass very large currents and are cased in aluminium with fins to increase surface area and promote heat loss.

Input and signal processing subsystems in electronic circuits rarely involve large currents, but power rating should be considered when circuits drive output transducers, such as lamps, LEDs, and loudspeakers.

 

 

Resistors in series and parallel

In a series circuit, the current flowing is the same at all points. The circuit diagram shows two resistors connected in series with a 6 V battery:

current the same at all pointsResistors in series

It doesn't matter where in the circuit the current is measured, the result will be the same. The total resistance is given by:

In this circuit, Rtotal=1+1=2 . What will be the current flowing? The formula is:

Substituting:

Notice that the current value is in mA when the resistor value is substituted in .

The same current, 3 mA, flows through each of the two resistors. What is the voltage across R1? The formula is:

Substituting:

What will be the voltage across R2? This will also be 3 V. It is important to point out that the sum of the voltages across the two resistors is equal to the power supply voltage.

The next circuit shows two resistors connected in parallel to a 6 V battery:

alternative pathways for current flowResistors in parallel

Parallel circuits always provide alternative pathways for current flow. The total resistance is calculated from:

product over sum formula

This is called the product over sum formula and works for any two resistors in parallel. An alternative formula is:

reciprocal formula

This formula can be extended to work for more than two resistors in parallel, but lends itself less easily to mental arithmetic. Both formulae are correct.

What is the total resistance in this circuit?

The current can be calculated from:

How does this current compare with the current for the series circuit? It's more. This is sensible. Connecting resistors in parallel provides alternative pathways and makes it easier for current to flow. How much current flows through each resistor? Because they have equal values, the current divides, with 6 mA flowing through R1, and 6 mA through R2.

To complete the picture, the voltage across R1 can be calculated as:

This is the same as the power supply voltage. The top end of R1 is connected to the positive terminal of the battery, while the bottom end of R1 is connected to the negative terminal of the battery. With no other components in the way, it follows that the voltage across R1 must be 6 V. What is the voltage across R2? By the same reasoning, this is also 6 V.