Current Electricity 5 Question 5
5. A resistance is shown in the figure. Its value and tolerance are given respectively by
(2019 Main, 9 April I)
(a) $270 \Omega, 5 %$
(b) $27 k \Omega, 20 %$
(c) $27 k \Omega, 10 %$
(d) $270 k \Omega, 10 %$
Show Answer
Solution:
- The value of a carbon resistor is given as,
$$ R=A B \times C \pm D % $$
where, colour band $A$ and $B$ (first two colours) indicate the first two significant figures of resistance in ohms, $C$ (third color) indicates the decimal multiplier and $D$ (forth colour) indicates the tolerance in $%$ as per the indicated value.
The table for colour code of carbon resistor is given below,
| Colour Codes |
Values $(\boldsymbol{A}, \boldsymbol{B})$ |
Multiplier $(\boldsymbol{C})$ | Tolerance $(\boldsymbol{D}) \mathbf{( % )})$ |
|---|---|---|---|
| Black | 0 | $10^{0}$ | |
| Brown | 1 | $10^{1}$ | |
| Red | 2 | $10^{2}$ | |
| Orange | 3 | $10^{3}$ | |
| Yellow | 4 | $10^{4}$ | |
| Green | 5 | $10^{5}$ | |
| Blue | 6 | $10^{6}$ | |
| Violet | 7 | $10^{7}$ | |
| Grey | 8 | $10^{8}$ | |
| White | 9 | $10^{9}$ | |
| Gold | $\pm 5 %$ | ||
| Silver | $\pm 20 %$ | ||
| No colour |
$\therefore$ Comparing the colors given in the question and the table and writing in the manner of
Eq. (i), we get
$$ \begin{aligned} R & =27 \times 10^{3} \Omega, \pm 10 % \\ & =27 k \Omega, \pm 10 % . \end{aligned} $$
