Question

The colour coding on a carbon resistor is shown in the given figure. The resistance value of the given resistor is : 

 

• A. (5700 \(\pm\) 375) \(\Omega\)
• B. (7500 \(\pm\) 750) \(\Omega\)
• C. (5700 \(\pm\) 285) \(\Omega\)
• D. (7500 \(\pm\) 375) \(\Omega\)

Hint:

A helpful mnemonic to remember the color code sequence is: "B B R O Y of Great Britain has a Very Good Wife". (Black, Brown, Red, Orange, Yellow, Green, Blue, Violet, Grey, White). Remember the tolerance bands Gold (5%) and Silver (10%) separately.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We need to determine the resistance and tolerance of a carbon resistor based on its four color bands: Violet, Green, Red, and Gold.
Step 2: Key Formula or Approach:
The resistance of a four-band resistor is given by the formula \( R = (AB \times 10^C) \pm D% \), where:
- A is the first significant digit (first band).
- B is the second significant digit (second band).
- C is the decimal multiplier (third band).
- D is the tolerance (fourth band).
We use the standard color code chart:
- Black(0), Brown(1), Red(2), Orange(3), Yellow(4), Green(5), Blue(6), Violet(7), Grey(8), White(9).
- Gold(\(\pm\)5%), Silver(\(\pm\)10%).
Step 3: Detailed Explanation:
Let's decode the given color bands:
- First band (A): Violet \(\rightarrow\) 7
- Second band (B): Green \(\rightarrow\) 5
- Third band (C, Multiplier): Red \(\rightarrow\) \(10^2\)
- Fourth band (D, Tolerance): Gold \(\rightarrow\) \(\pm\)5%
Now, we calculate the resistance value:
\[ R = (75 \times 10^2) \, \Omega = 7500 \, \Omega \] Next, we calculate the tolerance value:
Tolerance = D% of R
\[ \text{Tolerance} = 5% \text{ of } 7500 \, \Omega = \frac{5}{100} \times 7500 = 375 \, \Omega \] So, the resistance value of the given resistor is \( (7500 \pm 375) \, \Omega \).
Step 4: Final Answer:
The resistance value is (7500 \(\pm\) 375) \(\Omega\).