Animated Solution for Physics - Current Electricity: The colour coding on a carbon resistor is shown in the given figure. The resistance value of the given resistor is

Mastering Carbon Resistor Color Codes

Have you ever looked at a circuit board and wondered what those tiny, colorful cylinders are? Those are carbon resistors, and the colorful bands painted on them are not for decoration—they are a universal language! In this problem, we are going to decode this language step-by-step to find the exact resistance value of the given component.

To decode a carbon resistor, we use a standard color code table. A classic mnemonic to remember the sequence of colors is: "BB ROY of Great Britain had a Very Good Wife" (Black, Brown, Red, Orange, Yellow, Green, Blue, Violet, Gray, White).

For a standard four-band resistor, the rules are simple: 1. First Band: Represents the first significant digit. 2. Second Band: Represents the second significant digit. 3. Third Band: Represents the decimal multiplier (i.e., $10^n$). 4. Fourth Band: Represents the tolerance (the acceptable error margin in percentage).

Let's look at the resistor given in our problem. The bands, from left to right, are Violet, Green, Red, and Gold.

- First Band (Violet): According to our color chart, Violet corresponds to the number $7$. - Second Band (Green): Green corresponds to the number $5$.

Putting these together, our significant digits are $75$.

- Third Band (Red): Red corresponds to the number $2$. Since this is the multiplier band, it means we multiply our significant digits by $10^2$.

So, our base resistance is:

- Fourth Band (Gold): The Gold band indicates a tolerance of $\pm 5\%$.

This means the actual resistance can vary by $5\%$ above or below the base value of $7500\Omega$.

Here is where many students make a silly mistake! If you look at the options, the tolerance is not given as a percentage; it is given in absolute Ohms. We need to calculate exactly what $5\%$ of $7500\Omega$ is.

Let's do the math:

Now we combine our base resistance with our absolute tolerance. The final resistance value is:

This matches perfectly with option (d).

Pro-Tip: What if you encounter a resistor with only three bands? If the fourth band is missing, the tolerance defaults to $\pm 20\%$. Always keep an eye out for that missing band!