Resistors

We can control the current in electrical circuits using resistors. Of course, there are other means to achieve that control, but resistors are very simple, cheap, and efficient electronic components.

Control is the true magic word in electronics. No matter what we do, the purpose is to take control of voltages, currents, frequencies, and of various functions. Once we achieve total control, then we can do whatever we can think of.

There are few basic things we need to know about resistors:
1. Types of resistors
2. Useful formulas
3. Resistors colour code chart
4. Equivalent series and parallel resistors
5. Controlling voltage and current
6. Detecting current sense
7. Frequency control

Types of resistors

There is an incredible variety of resistors, here are just few main groups. First of all resistors are:
A. fixed
B. variable

Depending on the way we insert them into electrical circuits, resistors can be:
a. Through Hole (TH)
b. Surface Mount (SM)
c. Various, Mechanical Fixtures

Further, resistors are built as:
1. Carbon composition
2. Metal Film
3. Carbon Film
4. Wirewound

Of course we could differentiate resistors based on the power (current) they handle, but there are way too many types available.

Variable resistors come in few particular formats, and each type requires specific schematics:
1. Potentiometers
2. Rheostats
3. Decades
4. Programmable potentiometers

Fig1: Rheostat and Potentiometer wiring Schematics The Rheostat circuit is used to control (great) currents (Iv) The Potentiometer circuit is used to control voltages (Uv)

USEFUL FORMULAS

In order to work with resistors a few formulas are required such as:

• Resistance
• Ohm's Law in DC circuits
• Ohm's Law in AC circuits
• Impedance
• Resistance value at current temperature
• Conductance
• Electrical conductivity
• DC power
• Horse power conversion
• Kilowatt to hp conversion
• DC Energy
• Efficiency

RESISTORS COLOUR CODE CHART

Fixed resistors of the Through Hole type are marked with a special colour code.

The new SM (Surface Mount) types are marked with numbering systems specific to each manufacturer--please consult their Data Sheets.

NOTE
The third band is missing in most cases.

EQUIVALENT SERIES AND PARALLEL RESISTORS

The equivalent of series resistors is calculated with: R_T = Σ R_i
The equivalent of parallel resistors is calculated with: 1/R_T = Σ 1/R_i

Calculation examples for three resistors:

	Fig 2: The equivalent resistance of 3 series resistors RT = R1 + R2 + R3 RT = 2K +3K + 4K = 9K The series equivalent RT is greater than the greatest component
	Fig 3: The equivalent resistance of 3 resistors in parallel 1/RT = 1/R1 +1/R2 + 1/R3 RT = R1*R2*R3 / (R2*R3 + R1*R3 +R1*R2) RT = 24 / (12 + 8 + 6) = 24 / 26 = 0.923K The parallel equivalent RT is always smaller than the smallest component

CONTROLLING VOLTAGE AND CURRENT

	Fig 4: Voltage control circuit Voltage divider formula: Ui = (U * Ri) / RT U = 12 V Ri = 3Ω RT = 1Ω + 3Ω = 4Ω Ui = (12 * 3) / 4 = 9 V
	Fig 5: Current control circuit Imax = U / RLoad = 12 / 3 = 4 mA

In Fig 4 we control voltage U_i using a "voltage divider" schematic. We can even adjust U_i if we use a potentiometer schematic as we did in in Fig 1. The voltage divider schematic allows for 2, 3,..n precise voltage levels to be supplied to the Load circuit. Adjacent are the formulas used to calculate Ui value.

In Fig 5 R1 plays the role of a "current limiter". The meaning of that schematic is, the maximum current supplied to Load is 4 mA. Even if Load becomes a short-circuit, the maximum current will not exceed 4 mA. Please note: by using a variable resistor wired like in Fig 1, the Rheostat, we can even adjust the maximum limit current.

In both of the above schematics we could use programmable potentiometers. .

DETECTING CURRENT SENSE

Fig 6: Detecting current sense Possible cases: V1 > V2 Load is drawing power V1 = V2 Load is Open V1 < V2 Load is generating power V2 = 0 Load is short-circuited

In normal conditions V1 = 12 V, and V2 = 11.988 V (R1 = 1 KΩ). Those values are sent to the PIC controller Analog-to-Decimal channels 1 and 2 (randomly chosen). Next, we transform the analog voltages into their decimal equivalents, and we compare them mathematically. The result is one of the following cases:

V1 > V2 (Load is drawing power)
V1 = V2 (Load is Open)
V1 < V2 (Load is generating power)
V2 = 0 (Load is short-circuited)

If an accident happens and Load becomes generator, the current I will change its sense, then V2 will become greater than V1:
V2 > V1
Not only we are able to clearly detect current sense, but we know precisely how much current Load is drawing in each moment.