Question

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%

Answer 1

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%.