Question

The color code of a resistor is brown, black and brown. Then the value of resistance of
A. \[10\,\Omega \]
B. \[100\,{\text{m}}\Omega \]
C. \[0.1\,{\text{k}}\Omega \]
D. \[100 + 5\% \]

Answer 1

Hint:Recall the basics steps to determine the resistance on a three band resistor. Also, recall the values of the digits corresponding to the brown and black color band on the resistor and the multiplier corresponding to the brown color band on the resistor. Use the formula to determine the resistance on a three band resistor and calculate the required value of the resistance.

Formula used:
The resistance \[R\] of a three band resistor is given by
\[R = \left( {{1^{{\text{st}}}}{\text{ digit}} \times 10 + {2^{{\text{nd}}}}{\text{ digit}}} \right) \times {\text{Multiplier}}\] …… (1)
Here, \[{1^{{\text{st}}}}{\text{ digit}}\] is the digit related to first color on the resistor, \[{2^{{\text{nd}}}}{\text{ digit}}\] is the second digit related to the second color on the resistor and \[{\text{Multiplier}}\] is the multiplier related to the third color on the resistor.

Complete step by step answer:
We have given that the code on the resistor is brown, black and brown. We have asked to determine the value of the resistance of the resistor.There are some carbon composition or carbon film resistors which are very small. The value of the resistor cannot be written on these resistors. So there are color bands on these resistors. From these color bands, we can determine the resistance of that resistor.

For a three band resistor, there are three color bands on the resistor. The first color represents the first digit in the value of the resistance, the second color represents the second digit in the value of the resistance and the third color represents the multiplier of the value of resistance.

We know that the digit corresponding to the brown color band is 1. The digit corresponding to the black color band is 0 and the multiplier corresponding to the brown color band is 10.We can determine the resistance of the given resistor using equation (1). Substitute 1 for \[{1^{{\text{st}}}}{\text{ digit}}\], 0 for \[{2^{{\text{nd}}}}{\text{ digit}}\] and 10 for \[{\text{Multiplier}}\] in equation (1).
\[R = \left( {\left( 1 \right) \times 10 + \left( 0 \right)} \right) \times \left( {10} \right)\]
\[ \Rightarrow R = \left( {10 + 0} \right) \times \left( {10} \right)\]
\[ \Rightarrow R = 100\,\Omega \]
\[ \Rightarrow R = \left( {100\,\Omega } \right)\left( {\dfrac{{{{10}^{ - 3}}\,{\text{k}}\Omega }}{{1\,\Omega }}} \right)\]
\[ \therefore R = 0.1\,{\text{k}}\Omega \]
Therefore, the resistance of the given resistor is \[0.1\,{\text{k}}\Omega \].

Hence, the correct option is C.

Note: The students should correctly remember the values of the first and second digits corresponding to the color bands on the resistor and the multipliers corresponding to the third color band on the resistor. If one does not remember these values correctly then the final value of the resistance will not be correct.