Question

The unknown resistance R₄ measured in a Wheatstone bridge by the formula \({R_4} = {\frac{{{R_2}{R_3}}}{{{R_1}}}_{}}\)  with

R₁ = 100 ± 0.5% Ω,

R₂ = 1000 ± 0.5% Ω,

R₃ = 842 ± 0.5% Ω

resulting in R₄

1. 8420 ± 0.5% Ω
2. 8420 ± 1.0% Ω
3. 8420 ± 1.5% Ω
4. 8420 ± 0.125% Ω

Answer 1

Correct Answer - Option 3 : 8420 ± 1.5% Ω

\({R_4} = {\frac{{{R_2}{R_3}}}{{{R_1}}}_{}}\)

R1 = 100 ± 0.5% Ω,

R2 = 1000 ± 0.5% Ω,

R3 = 842 ± 0.5% Ω

Value of R₄

\({R_4} = {\frac{{{R_2}{R_3}}}{{{R_1}}}_{}}\)

\({R_4} = {\frac{{{1000}\times{842}}}{{{100}}}_{}}\)

R₄ = 8420 Ω 

Percentage limiting error:

\(\frac{{\partial {R_4}}}{{{R_4}}} =± \left( {\frac{{\partial {R_2}}}{{{R_2}}} + \frac{{\partial {R_3}}}{{{R_3}}} + \frac{{\partial {R_1}}}{{{R_1}}}} \right)\)

\(\frac{{\partial {R_4}}}{{{R_4}}} =±(0.5+0.5+0.5)\)

= ± 1.5%

R₄ = 8420 ± 1.5% Ω