Q.How can a resistance of $3700\,\Omega \pm 10\%$ be represented by colour code?

Using the standard 4-band resistor colour code, $3700\,\Omega\pm10\%$ is written as Orange–Violet–Red–Silver.

The standard colour code assigns digits to colours as: Black=0, Brown=1, Red=2, Orange=3, Yellow=4, Green=5, Blue=6, Violet=7, Grey=8, White=9; the tolerance colours are Gold=±5%, Silver=±10%.

Write $3700\,\Omega$ in the form (first two significant digits) × $10^{\text{power}}$:

$3700 = 37 \times 10^{2}$ …

±50 Ω on 500 Ω = ±10% tolerance → silver ring.

Red-Red-Red-Gold reads as $22 \times 10^2\ \Omega \pm 5\%$.

In the standard carbon-resistor colour code, the first two bands give the first two significant digits, the third band gives the power-of-ten multiplier, and the fourth band gives the tolerance. Red corresponds to the digit $2$, so the first two (red) bands give the digits $2$ and $2$, and the third (red) band gives a multiplier of $10^2$. A …

Each digit and the multiplier of a resistor's value is read off the standard colour code table, with the last band giving the tolerance.

In the four-band resistor colour code, the first two bands give the first two significant digits, the third band gives the power-of-ten multiplier, and the fourth band gives the tolerance.

Colour code table (digit / multiplier):

Black=0, Brown=1, Red=2, Orange=3, Yellow=4, Green=5, Blue=6, Violet=7, Grey=8, White=9.

Tolerance: Gold = ±5%, Silver = ±10%.

Write $3700\ \Omega$ as $37 \times 10^{2}\ \Omega$:

• 1st digit = 3 → Orange …

$42\,M\Omega \pm 20\%$ decodes to Yellow-Red-Blue with no tolerance band.

A carbon resistor is colour-coded using the standard digit table:

Black=0, Brown=1, Red=2, Orange=3, Yellow=4, Green=5, Blue=6, Violet=7, Grey=8, White=9; tolerance colours: Brown=±1%, Red=±2%, Gold=±5%, Silver=±10%, No colour = ±20%.

Given value: $R = 42\,M\Omega = 42\times 10^6\,\Omega$.

• 1st band (1st significant digit '4') → Yellow
• 2nd band (2nd significant digit '2') → Red
• 3rd band (multiplier, $10^6$) → Blue …

Brown-Black-Green-Gold decodes to $10\times10^5\,\Omega = 1\,\text{M}\Omega$ with $\pm5\%$ tolerance.

Colour code table (relevant colours):

Reading the bands (1st digit, 2nd digit, multiplier, tolerance):

• 1st band Brown -> first significant digit = 1
• 2nd band Black -> second significant digit = 0
• 3rd band Green -> multiplier = $10^5$
• 4th band Gold -> tolerance = $\pm5\%$

Computing the value. …