Limiting Error MCQ Quiz - Objective Question with Answer for Limiting Error - Download Free PDF

The correct answer is option 2):(1.81%)

Concept:

The magnitude of limiting error at full scale is given by  δA = ± 1% of Full Scale And the magnitude of relative error for a given voltage is calculated as: δ   

\(e_s=\frac{δ A}{A_s}\)   

A_s = Given the measured voltage

Calculation:

The magnitude of limiting error at full scale will be:

\(δ A=± \ 150\times\frac{1}{100}\)

δA = ± 1.5 V

This indicates that whatever we measure with this meter, there will be an error of 1.5 V.

Now, the relative limiting error for the reading of 83 V will be: δ

\(e_s=\frac{δ A}{A_s}=\frac{1.5}{83}\times 100\)

= 1.81 %

Concept:
Limiting error: The maximum allowable error in the measurement is specified in terms of true value, which is known as limiting error. It will give a range of errors. It is always with respect to the true value, so it is a variable error.

\({\rm{\% L}}imiting\;Error\;\left( {\% L.E.} \right){\rm{\;}} = \frac{{Limiting\;Error\;\left( {L.E.} \right)}}{{True\;value}} \times 100\)

Guaranteed accuracy error: The allowable error in measurement is specified in terms of full-scale value is known as guaranteed accuracy error. It is a variable error seen by the instrument since it is with respect to full-scale value.

\({\rm{\% Guaranteed\;accuracy\;error\;}} = \frac{{Limiting\;Error\;\left( {L.E.} \right)}}{{Full\;scale\;value}} \times 100\)

Calculation:

Full scale voltage = 200 V

Accuracy = 1%

Voltage to be measured = 50 V

The limiting error is given as :-

= \(\frac{1}{{100}} \times 200\times \frac{1}{{50}}\)

=4/100

= \(\frac{4}{{100}} \times 100 = 4\% \)

Full scale voltage = 150 V

Accuracy = 1%

Voltage to be measured = 75 V

The limiting error is given as :-

= \(\frac{1}{{100}} \times 150 \times \frac{1}{{75}}\)

=2/100

= \(\frac{2}{{100}} \times 100 = 2\% \)

Formula: 

\({\rm{\% Guaranteed\;accuracy\;error\;}} = \frac{{Limiting\;Error\;\left( {L.E.} \right)}}{{Full\;scale\;value}} \times 100\)

\({\rm{\% L}}imiting\;Error\;\left( {\% L.E.} \right){\rm{\;}} = \frac{{Limiting\;Error\;\left( {L.E.} \right)}}{{True\;value}} \times 100\)

Calculation:

Given-

Full scale reading = 200 A

Guaranteed accuracy = 1% of full-scale reading = 0.01 × 200 = 2 A

Measured value = 10 A

Limiting error \( = \frac{{2}}{{10}} \times 100 = 20\% \)

Concept:
Limiting error: The maximum allowable error in the measurement is specified in terms of true value, which is known as limiting error. It will give a range of errors. It is always with respect to the true value, so it is a variable error.

\({\rm{\% L}}imiting\;Error\;\left( {\% L.E.} \right){\rm{\;}} = \frac{{Limiting\;Error\;\left( {L.E.} \right)}}{{True\;value}} \times 100\)

Guaranteed accuracy error: The allowable error in measurement is specified in terms of full-scale value is known as guaranteed accuracy error. It is a variable error seen by the instrument since it is with respect to full-scale value.

\({\rm{\% Guaranteed\;accuracy\;error\;}} = \frac{{Limiting\;Error\;\left( {L.E.} \right)}}{{Full\;scale\;value}} \times 100\)

Calculation:

Full scale voltage = 200 V

Accuracy = 0.5%

Voltage to be measured = 50 V

The limiting error is given as:-

= \(\frac{0.5}{{100}} \times 200\times \frac{1}{{50}}\)

=2/100

= \(\frac{2}{{100}} \times 100 = 2\% \)

We know that,

\(\begin{array}{l} P = {I^2}R\\ R = \frac{P}{{{I^2}}}\\ \% \frac{{dR}}{R} = \pm \left( {\frac{{dP}}{P} + 2\frac{{dI}}{I}} \right) \times 100 \end{array}\)

Given that,

\(\begin{array}{l} \frac{{dP}}{P} = 0.02,\frac{{dI}}{I} = 0.0125\\ \% \frac{{dR}}{R} = \pm \left( {0.02 + 2\left( {0.0125} \right)} \right) \times 100 \end{array}\)

= ± 4.5%

Alternate Method:

When variables are in division (or) in multiplication form, we can add the corresponding percentage limiting errors.

Given that,

Limiting error of P = ± 2%

Limiting error of I = ± 1.25%

Limiting error or R = ?

We know that, \(R = \frac{P}{{{I^2}}}\)

= ± 2% + 2 (± 1.25%)

= ± 4.5%

Concept:

Limiting error: The maximum allowable error in the measurement is specified in terms of true value, is known as limiting error. It will give a range of errors. It is always with respect to the true value, so it is a variable error.

Guaranteed accuracy error: The allowable error in measurement is specified in terms of full-scale value is known as guaranteed accuracy error. It is a variable error seen by the instrument since it is with respect to full-scale value.

Calculation:

Given that, full-scale reading = 25 A

Guaranteed accuracy error = 1% of full-scale reading = 1% of 25 = 0.25 A

True value = 5 A

Limiting error \(= \frac{{0.25}}{5} = 0.05\)

Limitting error = 5%

The correct answer is option 2):(1.81%)

Concept:

The magnitude of limiting error at full scale is given by  δA = ± 1% of Full Scale And the magnitude of relative error for a given voltage is calculated as: δ   

\(e_s=\frac{δ A}{A_s}\)   

A_s = Given the measured voltage

Calculation:

The magnitude of limiting error at full scale will be:

\(δ A=± \ 150\times\frac{1}{100}\)

δA = ± 1.5 V

This indicates that whatever we measure with this meter, there will be an error of 1.5 V.

Now, the relative limiting error for the reading of 83 V will be: δ

\(e_s=\frac{δ A}{A_s}=\frac{1.5}{83}\times 100\)

= 1.81 %

Concept of Limiting error:

Limiting error is defined as the difference between the measured quantity (Am) and the true quantity (At).

Limiting error LE = Am - At 

%Limiting error (%LE):

It can be calculated as the ratio of limiting error to the true quantity.

%LE = \(\frac{A_m -A_t }{A_t } \times 100\)

Guaranteed accuracy error (GAE):

It can be calculated as the ratio of limiting error to the full-scale value.

% GAE = \(\frac{Limiting\ error}{Full\ scale\ reading}\times 100=\frac{A_m -A_t }{Full\ scale\ reading} \times 100\)

Calculation:

Given that,

Full-scale reading = 25 A

% GAE = 1 %

True value of ammeter = At

% GAE = \(\frac{L E}{FSR}\times 100=\frac{A_m -A_t }{FSR} \times 100\)

Where, FSR is Full scale reading

⇒ 1 = (Limiting error / 25 ) x 100

∴ Limiting error = 0.25 A

% LE = (Limiting error / True value) x 100

⇒ % LE = (0.25 / 5) x 100

∴ % Limiting error = 5 %

Concept:
Limiting error: The maximum allowable error in the measurement is specified in terms of true value, which is known as limiting error. It will give a range of errors. It is always with respect to the true value, so it is a variable error.

\({\rm{\% L}}imiting\;Error\;\left( {\% L.E.} \right){\rm{\;}} = \frac{{Limiting\;Error\;\left( {L.E.} \right)}}{{True\;value}} \times 100\)

Guaranteed accuracy error: The allowable error in measurement is specified in terms of full-scale value is known as guaranteed accuracy error. It is a variable error seen by the instrument since it is with respect to full-scale value.

\({\rm{\% Guaranteed\;accuracy\;error\;}} = \frac{{Limiting\;Error\;\left( {L.E.} \right)}}{{Full\;scale\;value}} \times 100\)

Calculation:

Full scale voltage = 200 V

Accuracy = 1%

Voltage to be measured = 50 V

The limiting error is given as :-

= \(\frac{1}{{100}} \times 200\times \frac{1}{{50}}\)

=4/100

= \(\frac{4}{{100}} \times 100 = 4\% \)

Concept:
Limiting error: The maximum allowable error in the measurement is specified in terms of true value, which is known as limiting error. It will give a range of errors. It is always with respect to the true value, so it is a variable error.

\({\rm{\% L}}imiting\;Error\;\left( {\% L.E.} \right){\rm{\;}} = \frac{{Limiting\;Error\;\left( {L.E.} \right)}}{{True\;value}} \times 100\)

Guaranteed accuracy error: The allowable error in measurement is specified in terms of full-scale value is known as guaranteed accuracy error. It is a variable error seen by the instrument since it is with respect to full-scale value.

\({\rm{\% Guaranteed\;accuracy\;error\;}} = \frac{{Limiting\;Error\;\left( {L.E.} \right)}}{{Full\;scale\;value}} \times 100\)

Calculation:

Full scale voltage = 200 V

Accuracy = 0.5%

Voltage to be measured = 50 V

The limiting error is given as:-

= \(\frac{0.5}{{100}} \times 200\times \frac{1}{{50}}\)

=2/100

= \(\frac{2}{{100}} \times 100 = 2\% \)

Full scale voltage = 150 V

Accuracy = 1%

Voltage to be measured = 75 V

The limiting error is given as :-

= \(\frac{1}{{100}} \times 150 \times \frac{1}{{75}}\)

=2/100

= \(\frac{2}{{100}} \times 100 = 2\% \)

Formula: 

\({\rm{\% Guaranteed\;accuracy\;error\;}} = \frac{{Limiting\;Error\;\left( {L.E.} \right)}}{{Full\;scale\;value}} \times 100\)

\({\rm{\% L}}imiting\;Error\;\left( {\% L.E.} \right){\rm{\;}} = \frac{{Limiting\;Error\;\left( {L.E.} \right)}}{{True\;value}} \times 100\)

Calculation:

Given-

Full scale reading = 200 A

Guaranteed accuracy = 1% of full-scale reading = 0.01 × 200 = 2 A

Measured value = 10 A

Limiting error \( = \frac{{2}}{{10}} \times 100 = 20\% \)

Limiting error:

Limiting error is defined as the difference between the measured quantity (Am) and the true quantity (At).

Limiting error LE = Am - At 

%Limiting error (%LE):

It can be calculated as the ratio of limiting error to the true quantity.

%LE = \(\frac{A_m -A_t }{A_t } \times 100\)

Guaranteed accuracy error (GAE):

It can be calculated as the ratio of limiting error to the full-scale value.

% GAE = \(\frac{Limiting\ error}{Full\ scale\ reading}\times 100=\frac{A_m -A_t }{Full\ scale\ reading} \times 100\)

Calculation:

GIven that,

Full-scale reading =10 A

% GAE = 1 %

True value of ammeter = At

% GAE = \(\frac{Limiting\ error}{Full\ scale\ reading}\times 100=\frac{A_m -A_t }{Full\ scale\ reading} \times 100\)

⇒ 1 = (Limiting error / 10 ) x 100

∴ Limiting error = 0.1 A

% LE = (Limiting error / True value) x 100

⇒ % LE = (0.1 / 2.5) x 100

∴ % Limiting error = 4 %

Concept:

Limiting error: The maximum allowable error in the measurement is specified in terms of true value, is known as limiting error. It will give a range of errors. It is always with respect to the true value, so it is a variable error.

Guaranteed accuracy error: The allowable error in measurement is specified in terms of full-scale value is known as guaranteed accuracy error. It is a variable error seen by the instrument since it is with respect to full-scale value.

Calculation:

Given that, full-scale reading = 25 A

Guaranteed accuracy error = 1% of full-scale reading

= 1% of 25 = 0.25 A

True value = 10 A

% Limiting error will be:

\(\%L= \frac{{0.25}}{10}\times 100\)

%L = 2.5 %