Question

An ammeter of 0-50 A range has an accuracy of ± 1% of full scale reading. The current measured is 10 A. The uncertainty in measured value is
1. ± 2%
2. ± 2.5%
3. ± 4%
4. ± 5%

Answer 1

Correct Answer - Option 4 : ± 5%

Concept:

Uncertainly of combination of component:

It is a deviation of the measured value from a unique sample of data specified in terms of the degree of confidence of the user.

Let X = f (x₁, x₂, …….x_n)

Then uncertainly is

\({w_x} = \sqrt {{{\left( {\frac{{\partial x}}{{\partial {x_1}}}} \right)}^2}wx_1^2 + {{\left( {\frac{{\partial x}}{{\partial {x_2}}}} \right)}^2}wx_2^2 + \ldots {{\left( {\frac{{\partial x}}{{\partial {x_n}}}} \right)}^2}wx_n^2} \)

Where wx₁, wx₂, ….wx_n are uncertainly of x₁, x₂, x_n

Calculation:

According to above concept

Let I = f(i) so \({w_I} = \frac{{\partial I}}{{\partial i}}{w_i}_1\)

Then Given, ∂I = 50 A, 2i = 10 A, \({w_i}_1 = \pm 1\% \)

So \({w_I} = \frac{{\partial I}}{{\partial i}}{w_i}_1 = \frac{{50}}{{10}} \times \left( { \pm 1\% } \right) = 5\% \)

So W_I = ±5% option 4 correct choice

More information:

Equivalent limiting error of some combinations:

I. Sum of the difference between two or more Quantities.

Let X = ± x₁ ± x₂ ± x₃

Then \(\frac{{\delta X}}{X} = \pm \left( {\frac{{{x_1}}}{X}\frac{{\delta {x_1}}}{{{X_1}}} + \frac{{{x_2}}}{X}\frac{{\delta {x_2}}}{{{X_2}}} + \frac{{{x_3}}}{X}\frac{{\delta {x_3}}}{X}} \right)\)

± δx₁→ Relative increment in quality x_i

± δx → Relative increment in X

\(\frac{{{\rm{\delta }}{x_i}}}{{{X_i}}}\) → Relative limiting error in quantity x_i

\(\frac{{{\rm{\delta }}X}}{X}\) → Relative limiting error in X

II. Product or Quotient of two or more quantity

Let \(X = {x_1}{x_2}{x_3}\;or\;X = \frac{{{x_1}}}{{{x_2}{x_3}}}\;or\;X = \frac{1}{{{x_1}{x_2}{x_3}}}\)

\(\frac{{{\rm{\delta }}X}}{X} = \pm \left( {\frac{{{\rm{\delta }}{x_1}}}{{{x_1}}} + \frac{{{\rm{\delta }}{x_2}}}{{{x_2}}} + \frac{{{\rm{\delta }}{x_3}}}{{{x_3}}}} \right)\)

III. Composite Factor:

Let \(X = x_1^nx_2^n\)

\(\frac{{{\rm{\delta }}X}}{X} = \pm \left( {\frac{{n{\rm{\delta }}{x_1}}}{{{x_1}}} + \frac{{m{\rm{\delta }}{x_2}}}{{{x_2}}}} \right)\)