Error Analysis MCQ Quiz in मल्याळम - Objective Question with Answer for Error Analysis - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

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:

In ammeters, the sensitivity \(S = \frac{1}{{{I_{fsd}}}}\)

I_fsd is the full-scale deflection in amps

It is expressed in ohm/volt

Calculation:

Full scale deflection = 20 μA

Precision: It is a measure of the reproducibility of the measurements, i.e. given a fixed value of quantity. It is a measure of the degree of agreement within a group of measurements.

Reproducibility: It is the degree of closeness with which given value may be repeatedly measured. It may be specified in terms of units for a given period of time.

Perfect reproducibility means that the instrument has no drift.

No drift means that with a given input the measured values do not vary with time.

Repeatability:

Reproducibility and repeatability are a measure of closeness with which a given input may be measured over and over again. Reproducibility is specified in terms of scale readings over a given period of time. Repeatability is defined as the variation of scale reading and is random in nature.

Instrumentation Errors:

These errors arise due to three main reasons:

• Instrumental errors occur due to the wrong construction of the measuring instruments.
• These errors may occur due to hysteresis or friction.
• These types of errors include the loading effect and misuse of the instruments.

Environmental Errors: These errors are due to conditions external to the measuring device including conditions in the area surrounding the instrument. These may be effects of temperature, pressure, humidity, dust, vibrations or of an external magnetic or electrostatic field.

Observational Errors: These types of errors occur due to wrong observations or reading in the instruments. The wrong observations may be due to parallax. In order to reduce the parallax error highly accurate meters are needed. Ex: meters provided with mirror scales.

R₁ = 100 Ω ± 5 Ω

R₂ = 150 Ω ± 15 Ω

R = R₁ + R₂

\(\begin{array}{l} \frac{{\partial R}}{{{R_1}}} = 1,\;{\sigma _1} = 5\\ \frac{{\partial R}}{{{R_2}}} = 1,\;{\sigma _2} = 15 \end{array}\)

Standard deviation of R is,

\(\sigma = \sqrt {{{\left( {\frac{{\partial R}}{{\partial {R_1}}}} \right)}^2}\sigma _1^2 + {{\left( {\frac{{\partial R}}{{\partial {R_2}}}} \right)}^2}\sigma _2^2}\)

\( = \sqrt {{{\left( 1 \right)}^2}{{\left( 5 \right)}^2} + {{\left( 1 \right)}^2}{{\left( {15} \right)}^2}} \)

= 15.8

Error (E):

The difference of magnitude between measured value (A_m) and true value (A_t) is called Error.

In engineering, the error is represented with ±.

In general, the error means Absolute Error it has only magnitude.

E = |A_m - A_t|

Percentage error is given as

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

Application:

Given,

A_m = 48 V

A_t = 50 V

From above concept,

E = |48 - 50| = 2 V

\(\%E=\dfrac{2}{50}\times100=4\ \%\)

The performance characteristics of an instrument are mainly divided into two categories: 

i) Dynamic characteristics 

ii) Static characteristics 

Dynamic characteristics: 

The set of criteria defined for the instruments, which are changing rapidly with time, is called ‘dynamic characteristics’. The various dynamic characteristics are:

 i) Speed of response

 ii) Measuring lag

 iii) Fidelity

iv) Dynamic error

Static characteristics: 

The set of criteria defined for the instruments, which are used to measure the quantities which are slowly varying with time or mostly constant, i.e., do not vary with time, is called ‘static characteristics’. 

The various static characteristics are: 

i) Accuracy  
ii) Precision  
iii) Sensitivity  
iv) Linearity  
v) Reproducibility  
vi) Repeatability  
viii) Threshold  
ix) Drift  
x) Stability  
xi) Tolerance  
xii) Range or span  

Voltmeter Sensitivity (S_v):

The voltmeter sensitivity is determined by dividing the sum of the resistance of the meter (Rm), plus the series resistance (Rs), by the full-scale reading in volts.

Mathematically, sensitivity is expressed as:

\(S_v=\frac{R_m+R_s}{E}\)

Expressing the above expression in units, we get:

\(S_v=\frac{Ohms}{Volt}\)

Voltmeter sensitivity is expressed in Ohm/Volt

Sensitivity is also expressed as:

\(S_v=\frac{1}{I_{FSD}}\)

So, sensitivity is said to be equal to the reciprocal of the full-scale deflection current.

Application:

Sensitivity, S_v = 1000 Ω/V

\({{\rm{I}}_{{\rm{FSD}}}} = \frac{1}{{\rm{S_v}}} = \frac{1}{{1000}} = 1{\rm{mA}}\)

At half full scale the current reading will be = 0.5 mA

Full scale voltage = 300 V

Accuracy = 2%

Voltage to be measured = 200 V

The limiting error is given as :-

= \(\frac{2}{{100}} \times 300 \times \frac{1}{{200}}\)

= 6/200

2% of limiting error

= \(\frac{6}{{200}} \times 100 = 3\% \)

OR
\(\)Limiting error= \(\frac {\%Guaranteed\ accuracy\times FSR}{Measured\ value}\)= \( \frac{2\times300}{200}=3\%\)