Current Electricity 5 Question 6
6. A carbon resistance has a following color code. What is the value of the resistance?
(a) $5.3 M \Omega \pm 5 %$
(b) $64 k \Omega \pm 10 %$
(c) $6.4 M \Omega \pm 5 %$
(d) $530 k \Omega \pm 5 %$
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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 colour) indicates the first two significant figures of resistance in Ohms.
$C$ (third colour) indicate the decimal multiplies and $D$ (fourth colour) indicates the tolerance in $%$ as per the indicated value. The table for colour code,
| Colour code | Values $(\boldsymbol{A B})$ |
Multiplier $(\boldsymbol{C})$ |
Tolerance |
|---|---|---|---|
| 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 | $10^{6}$ | |
| Voilet | 7 | $10^{7}$ | |
| Grey | 8 | $10^{8}$ | |
| White | 9 | $10^{9}$ | |
| Gold | - | - | $\pm 5 %$ |
| Silver | - | - | $\pm 10 %$ |
| No colour | - | - | $\pm 20 %$ |
$\because$ Comparing the colours given in the question and table and writing in the manner of Eq. (i), we get
$$ \begin{aligned} R & =53 \times 10^{4} \pm 5 % \Omega \\ \text { or } \quad R & =530 \times 10^{3} \Omega \pm 5 % \text { or } R=530 k \Omega \pm 5 % \end{aligned} $$
