Question

A resistor with the colour coded value of \[1000\] ohms and \[10%\] tolerance can have an actual resistance between
A.\[900ohms\,\text{and}\,1100ohms\]
B.\[900ohms\,\text{and}\,1010ohms\]
C.\[990ohms\,\text{and}\,1010ohms\]
D.\[900ohms\,\text{and}\,1000ohms\]

Answer 1

Hint:The color coding of the resistor gives the range of the value of the resistance the resistance can attain. When electric current is passed through the resistance then due to heat generated in the resistor there is change in the dimensions of the resistor which leads to the variation of the resistance value.


Complete step-by-step solution:
The resistance value as per the color coding is given as $1000\Omega $
The value of the tolerance of the resistor is 10%
The tolerance value of the resistor decides the range of the value of the resistor.
Actual value of the resistance, $R=$Value of the resistance$\pm $error
10% of the tolerance for the $1000\Omega $ resistance shows the variation of the value of the resistance about the given value of the resistance.
Error $=\pm 10%\text{ of }1000\Omega $
$\begin{align}
  & =\pm \frac{10}{100}\times 1000\Omega \\
 & =\pm 100\Omega \\
\end{align}$
Hence, the actual value of the resistance is given as,
$R=\left( 1000\pm 10 \right)\Omega $
Therefore the range of the value of the resistance can be calculated as,
between 900$\Omega $ and 1100$\Omega $.


Note:->The variation of the resistance value of the resistor is due to the heating effect of the electric current.
->When heat is generated then due to thermal expansion of the resistor material there is change in the dimension of the resistor which leads to the variation in the value of the actual value of the resistance.