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) $270 k \Omega, 10 %$

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Solution:

  1. 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

$$ \begin{aligned} R & =27 \times 10^{3} \Omega, \pm 10 % \\ & =27 k \Omega, \pm 10 % . \end{aligned} $$



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