The possible percentage error in computing the parallel resistance R of three resistances R1,R2,R3 from the formula 1R=1R1+1R2+1R3, if R1,R2,R3 are each in error by 1.2%

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Q.

The possible percentage error in computing the parallel resistance $R$ of three resistances $R_{1}, R_{2}, R_{3}$ from the formula $\frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}, if R_{1}, R_{2}, R_{3}$ are each in error by $1.2 %$

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a

1.2

b

1.7

c

1.3

d

1.4

answer is A.

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Detailed Solution

$\frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}$ differentiation on both sides

$- \frac{1}{R^{2}} Δ R = - \frac{1}{R_{1}^{2}} Δ R_{1} - \frac{1}{R_{2}^{2}} Δ R_{2} - \frac{1}{R_{3}^{2}} Δ R_{3}$

$∴ \frac{Δ R}{R} \times 100 = 1.2$

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