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Q.

Two resistors of $10 KΩ and 20 KΩ$ are connected in series. If tolerance of each resistor is 10% then tolerance of the combination will be

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a

10%

b

20%

c

5%

d

15%

answer is B.

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Detailed Solution

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$\begin{array}{l} R_{1} = 10 kΩ R_{2} = 20 kΩ \\ \frac{{ΔR}_{1}}{R_{1}} = 10 % \frac{{ΔR}_{2}}{R_{2}} = 10 % \\ R_{S} = R_{1} + R_{2} \\ \frac{{ΔR}_{s}}{R_{s}} = \frac{{ΔR}_{1} + {ΔR}_{2}}{R_{1} + R_{2}} \\ = \frac{1 \times 10^{3} + 2 \times 10^{3}}{10 \times 10^{3} + 20 \times 10^{3}} = \frac{3}{30} = \frac{1}{10} \\ % \frac{{ΔR}_{s}}{R_{s}} = \frac{1}{10} \times 100 = 10 % \end{array}$

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