Accuracy:
Accuracy indicates the degree of closeness of the measured quantity to the true value.
Which is more accurate?
a) ± 1%
b) ± 3%
c) ± 5%
d) ± 7%
Option a) is more accurate because ± 1% is close to the true value which means it has a very low error.
We call this a Guaranteed Accuracy Error.
Guaranteed Accuracy Error(G.A.E):
- Guaranteed Accuracy Error is specified by the manufacturer.
- Guaranteed Accuracy Error is always concerning the true value.
- This error is constant since the full-scale value is constant.
Example problem:
A (0-100)V voltmeter with a G.A.E Guaranteed Accuracy Error of ± 1%. If we measure a true value of 20V with this meter then the %L.E Limitting Error is
100 * ± 1 / 100 = ± 1V
At(True value) = 20V
20 * x / 100 = ± 1V
x = ± 5%
Therefore %L.E = ± 5%
Similarly when we have a true value = 25 V
then we get,
25 * x / 100 = ± 1V
x = ± 4%
Therefore %L.E = ± 4%
Similarly when we have a true value = 50 V
then we get,
50 * x / 100 = ± 1V
x = ± 2%
Therefore %L.E = ± 2%
Similarly when we have a true value = 100 V
then we get,
100 * x / 100 = ± 1V
x = ± 1%
Therefore %L.E = ± 1%
From this, we came to know that as the true value increases, the limitting error decreases whereas the G.A.E remains constant.
Note: Limitting error is concerning the true value and G.A.E is concerning the full-scale value.
While taking a reading in an instrument when the pointer moves towards the full-scale value, then the limitting error decreases which in turn increases the accuracy.
Precision:
- The most repeatable value or reproducible value out of the set of readings is called precision.
- We need accuracy as well as precision in an instrument.
- Precision characteristics should be the supporting characteristics of accuracy.
- Accurate instrument can be precise but precise instrument cannot be accurate.
Linearity:
The output follows the input with linear relation or linear equation is called linearity.
In general, we have only one meter which is called a theta meter. From this meter, we design everything by simply changing the scale value for the meters.
For any instrument, the input quantity is current which is then converted into force which is again converted into theta which means the angle of deflection the pointer shows.
All electrical instruments are energy converters that convert electrical energy into mechanical energy.
All electrical instruments work on the basic law of conservation of energy which means energy can neither be created nor be destroyed it can only be transferred from one place to another.
Scaling is one that converts mechanical θ deflection into electrical values.
The instruments have been chosen based on linearity or non-linearity.
Linear and nonlinear graph
Linear means
Linear Scale
Question:
When the true value is 18A, which ammeter will you choose when all scaling is linear?
a) (0-100)A
b) (0-20)A
c) (0-30)A
Sensitivity:
We prefer to use highly sensitive instruments so that we may not lose accuracy.
Sensitivity is also a supporting characteristics of accuracy.
It is the ratio of change in output to the change in input.
S = change in output / change in input
= slope
= tan θ
For a perfectly linear graph always θ is 45.
So we get tan 45 as 1.
It means that the sensitivity is 1 for all linear instruments.
Example: PMMC
Question:
Find the voltmeter reading across the resistor 50Ω using the voltmeter V1 and V2 with the sensitivity of 10 Ω/ V and 1000Ω /V respectively.
Let's find out the loading error and we will make comparison on both the values.
For first case,
% R.S.E = (23.80-25) / 25 * 100
= -4.8%
For second case,
% R.S.E = (24.98-25) / 25 * 100
= -0.08%
From this problem, we came to know that if the sensitivity increases, the loading error will decrease which in turn increases the accuracy.