Method used to calculate the errors in an instrumentt, The DC-Voltmeter and multi range voltmeter and operation. ,DC-Voltmeter,Multi range Voltmeter:

     Method used to calculate the errors in an instrument:-

ERROR IN MEASUREMENT:

Measurement is the process of comparing an unknown quantity with an accepted standard quantity.  

It involves connecting a measuring instrument into the system under consideration and observing the resulting response on the instrument. 


The measurement thus obtained is a quantitative measure of the so-called "true value" (since it is very difficult to define the true value, the term ''expected value" is used). 


Any measurement is affected by many variables; therefore the results rarely reflect the expected value. 
For example, connecting a measuring instrument into the circuit under consideration always disturbs (changes) the circuit, causing the measurement to differ from the expected value. Some factors that affect the measurements are related to the measuring instruments themselves.

Other factors are related to the person using the instrument. The degree to which a measurement nears the expected value is expressed in terms of the error of measurement. Error may be expressed either as absolute or as percentage of error. 

Absolute error may be defined as the difference between the expected

value of the variable and the measured value of the variable, or

e = Y n - X n

Where ,
e=absolute errors;

Yn=expected value;

Xn=measured value;

Therefore %error = (absolute value/expected value )*100=(e/Yn)*100

Therefore %error=

It is more frequently expressed as an accuracy rather than error.

Therefore A=1-

Where A is the relative accuracy 

Accuracy is expressed as % accuracy 

a=100%-%error

a=A*100% (where a=%accuracy)

The DC-Voltmeter and multi range voltmeter and operation.

A basic D'Arsonval movement can be converted into a dc voltmeter by adding a series resistor known as multiplier, as shown in the figure. The function of the multiplier is to limit the current through the movement so that the current does not exceed the full scale deflection value.

A dc voltmeter measures the potential difference between two points in a dc circuit or a circuit component. To measure the potential difference between two points in a dc circuit or a circuit component, a dc voltmeter is always connected across them with the proper polarity. The value of the multiplier required is calculated as follows.

Im: full scale deflection current of the movement

Rm : internal resistance of movement

Rs : Multiplier resistance

V: full range voltage of the instrument

From the circuit of Fig.

V= Im *( Rm+ Rs)

Rs = = -

therefore Rs = -

The multiplier limits the current through the movement, so as to not exceed the value of the full scale deflection Ifsd.

The above equation is also used to further extend the range in DC voltmeter'.

Multi range Voltmeter:

 Across the movement with a multi-position switch. As in the case of an ammeter, to obtain a multi range ammeter, a number of shunts are connected  resistors (multipliers) along with a range switch Similarly, a dc voltmeter can be converted into a multi range voltmeter by connecting a number of  to provide a greater number of workable ranges. The below Figure shows a multi range voltmeter using a three position switch and three multipliers R1, R2, and R3, for voltage values V1, V2, and V3. Fig

it can be further modified to multipliers connected in series string, which is a more practical arrangement of the multiplier resistors of a multi range voltmeter. In this arrangement, the multipliers are connected in a series string, and the range selector selects the appropriate amount of resistance required in series with the movement.

This arrangement is advantageous compared to the previous one, because all multi1llier resistances except the first have the standard resistance value and are also easily available in precision tolerances. The first resistor or low range multiplier, R4, is the only special resistor which has to be specially manufactured to meet the circuit requirements.