Animated Solution for Physics - Current Electricity: A carbon resistance has a following color code. What is the value of the resistance?

Have you ever looked at a tiny resistor on a circuit board and wondered what those colorful little stripes mean? They aren't just for decoration! Those bands are a universal language—a secret code that tells you exactly how much resistance that tiny component offers.

Today, we are going to crack that code together. I know memorizing tables can feel tedious, but once you understand the rhythm of it, it becomes second nature. Let's dive in!

Imagine you are holding the resistor from our problem. You see four distinct bands: Green, Orange, Yellow, and Golden.

The standard rule for a four-band resistor is beautifully simple. The first two bands give us our significant digits. The third band acts as a decimal multiplier, and the final, fourth band tells us the tolerance (how precise the manufacturing is).

To decode the colors, we use a classic mnemonic: "BB ROY of Great Britain had a Very Good Wife".

Each capitalized letter corresponds to a color and a number from 0 to 9: - Black (0), Brown (1) - Red (2), Orange (3), Yellow (4) - Green (5) - Blue (6) - Violet (7), Gray (8), White (9)

Let's apply this to our resistor!

Our first band is Green. Counting through our mnemonic, Green corresponds to the number 5.

Our second band is Orange. Orange corresponds to the number 3.

So, our base two-digit number is simply 53.

Now for the third band: Yellow. The third band is the multiplier, meaning we multiply our base number by $10$ raised to the power of the color's value. Yellow is 4, so our multiplier is $10^4$.

This gives us a raw resistance of:

Finally, the fourth band is Golden. Gold represents a tolerance of $\pm 5\%$. (Remember: Gold is precious, so it has a tight 5% tolerance. Silver is 10%, and no band is 20%).

So our complete expression is:

If we look at our options, they are in kilo-ohms ($\text{k}\Omega$) and mega-ohms ($\text{M}\Omega$). Let's format our answer to match.

We can rewrite $53\times 10^4$ by shifting the decimal:

Since $10^3\Omega$ is exactly $1\text{ k}\Omega$, we get:

And there we have it! The secret code is broken, and we've found our perfect match. Physics is just about learning the language of the universe, one color band at a time!