A wide variety of resistors, fixed or variable, are large enough to have
their resistance in ohms printed on the casing. Some, however, are too
small to have numbers printed on them, so a system of color coding is
used. For the thin-film resistor, four, five, or six bands may be used.
**Fig.No.1: **Color coding for fixed resistors.
**Fig.No.2: **Color coding
#### Four-band scheme

For the four-band scheme, the bands are always read from the end
that has a band closest to it, as shown in (Fig.No.1). The bands are numbered
as shown in (Fig.no.2) for reference in the discussion to follow.
**Example 1:** Find the value of the resistor in Fig.No.1.

**Solution:** Reading from the band closest to the left edge, we find that
the first two colors of red and black represent the numbers 2 and 0,
respectively as shown in (Fig.no.2). The third band is brown, representing the number 1 for the power of the multiplier as follows:
$$ 20 \times 10^1Ω = 200Ω$$
Now for the fourth band of gold, representing a tolerance of 5%:
To find the range into which the manufacturer has guaranteed the resistor
will fall, first convert the 5% to a decimal number equals to 0.05. Then multiply the resistor value by this decimal number:
$$0.05(200) Ω = 10 Ω$$
Finally, add the resulting number to the resistor value to determine the
maximum value, and subtract the number to find the minimum value.
That is,
$$ \text{Maximum} = 200Ω + 10Ω = 210 Ω$$
$$ \text{Minimum} = 200Ω - 10Ω = 190Ω$$
Range = 190 Ω to 210 Ω
Using the above procedure, the smallest resistor that can be labeled
with the color code is 10 Ω.
**Example 2:** Find the value of the resistor in Fig.No.3.

**Solution:** The first two colors are gray and red, representing the numbers
8 and 2, respectively. The third color is gold, representing a multiplier
of 0.1.
**Fig.no.3: **Example no.2
Using the multiplier, we obtain a resistance of
$$(0.1)(82 Ω) = 8.2 Ω$$
The fourth band is silver, representing a tolerance of 10%. Converting
to a decimal number and multiplying through yields 10% = 0.10 and
$$(0.1)(8.2Ω ) = 0.82Ω $$
$$\text{Maximum} = 8.2 Ω + 0.82 Ω = 9.02 Ω$$
$$\text{Minimum} = 8.2 Ω - 0.82 Ω = 7.38 Ω$$
so that Range = 7.38 Ω to 9.02 Ω
*The same color scheme to represent numbers is used for all the
important elements of electrical circuits. E.g Capacitor and Inductors.*
#### Five-band Color Code

**Fig.no.4: **Five-band color coding for fixed resistors.
Some manufacturers prefer to use a five-band color code. In such
cases, as shown in the top portion of Fig. No.4, three digits are provided
before the multiplier. The fifth band remains the tolerance indicator. If
the manufacturer decides to include the temperature coefficient, a sixth
band will appear as shown in the lower portion of Fig. No.4, with the
color indicating the PPM level.
For four, five, or six bands, if the tolerance is less than 5%, the following
colors are used to reflect the % tolerances:

*The first two bands represent the first and second digits, respectively. They are the actual first two numbers that define the numerical value of the resistor.*

*The third band determines the power-of-ten multiplier for the first
two digits (actually the number of zeros that follow the second digit
for resistors greater than 10 *Ω).

*The fourth band is the manufacture's tolerance, which is an indication
of the precision by which the resistor was made.
If the fourth band is omitted, the tolerance is assumed to be 20%.*

**However, the range can be extended to include resistors from 0.1 Ω to 10 Ω by
simply using gold as a multiplier color (third band) to represent 0.1
and using silver to represent 0.01.**

*brown = $\pm 1\%$, red = $\pm 2\%$, green = $\pm0.5\%$, blue = $\pm 0.25\%$, and violet = $\pm 0.1\%$.*