Question

What formula is used to calculate resistance using the color code?

Answer 1

Resistors

Resistors used may be wire bond or carbon resistors. Carbon resistors are inexpensive and compact. Color codes are present on carbon resistors in the form of co-axial bands. Digit values are considered from first two colors. third color is the multiplication factor. Forth color gives tolerance of the resistor.

Explanation

Formula is used to calculate resistance using the color code is: $R=\left[(10x+y)z\right]\pm \frac{p}{100}\Omega$, Here

1. x represents the first digit of the numerical value of the resistance, with respect to the first color band (A) .
2. y represents the second digit of the numerical value of resistance, with respect to the second color band (B).
3. z is the decimal multiplier and gives the number of zero after two digits, with respect to the third color (C).
4. p last shows the tolerance in percentage, with respect to the forth color (D).

For carbon resistors the values of A, B, C and D are given in the following table.

Example: Consider the color code of the resistor shown here.

1. First color (band A) is red. Digit for red is 2 in the table. So first digit of the resistance is 2.
2. Second color is orange, so second digit is 3.
3. Third color is yellow that has multiplication value 10000. So value of multiplier is 10000.
4. Forth color is silver, that has tolerance 10%.
5. Now final value of resistance is

$$\begin{gathered} R=\left[(10x+y)z\right]\pm \frac{p}{100}\Omega \\ =\left[\left(10x2+3\right)x10000\right]\pm \frac{10}{100} \\ =230000\pm 10\%\Omega \end{gathered}$$