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Q.

The value of two resistors are $(5 \cdot 0 \pm 0 \cdot 2) kΩ$ and $(10 \cdot 0 \pm 0 \cdot 1) kΩ$ What is the percentage error in the equivalent resistance when they are connected in parallel ?

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a

10%

b

7%

c

2%

d

5%

answer is C.

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Detailed Solution

$\begin{array}{l} \frac{Δ r}{r} = \frac{Δ r_{1}}{r_{1}} + \frac{Δ r_{2}}{r_{2}} + \frac{Δ r_{1} + Δ r_{2}}{r_{1} + r_{2}} \\ ∴ \frac{Δ r}{r} = \frac{0 \cdot 2}{5 \cdot 0} + \frac{0 \cdot 1}{10 \cdot 0} + \frac{0 \cdot 2 + 0 \cdot 1}{5 \cdot 0 + 10 \cdot 0} \\ = \frac{0 \cdot 2}{5} + \frac{0 \cdot 1}{10} + \frac{0 \cdot 3}{15} = 0 \cdot 07 \\ = 7 % \end{array}$

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