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A resistor of 10 kΩ with a tolerance of 5% is connected in parallel with 5 kΩ resistors of 10% tolerance. The tolerance limit is __________(a) 9%(b) 12.4%(c) 8.33%(d) 7.87%This question was addressed to me by my school teacher while I was bunking the class.Query is from Problems Involving Coupling Coefficient in chapter Resonance & Magnetically Coupled Circuit of Network Theory

Answer»

Correct choice is (c) 8.33%

To elaborate: Here, R1 and R2 are in parallel.

Then, \(\frac{1}{R} = \frac{1}{R_1}+ \frac{1}{R_2}\)

Or, R = \(\frac{50}{15}\) kΩ

∴\(\frac{△R}{R} = \frac{△R_1}{R_1^2} + \frac{△R_2}{R_2^2}\)

And △R1 = 0.5 × 10^3,△R2 = 0.5 × 10^3

∴ \(\frac{△R}{R} = \frac{10 × 10^3}{3 × 10 × 10^3} × \frac{0.5 × 10^3}{10 × 10^3} + \frac{10}{3} × \frac{10^3}{5 × 10^3} × \frac{0.5 × 10^3}{5 × 10^3}\)

= \(\frac{0.5}{30} + \frac{1}{15}= \frac{2.5}{30}\) = 8.33%.



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