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Engineering, HSC and IIT-JEE Mains and
Advanced videos.Hello Friends,In this video we will
study what is an error in measurement so
let us start with the topic.
Whenever we are doing any measurement
then we use a measuring device or a
measuring instrument to get the value of
the unknown quantity now any type of
measurement which is done with the help
of measuring instrument that will be
approximate because when we are
measuring a same thing again and again
then they may be possible that we get
different readings further from the
instrument okay
so measurement if we define that what is
measurement measurement is to get the
value of the unknown quantity
now to get this value of the unknown
quantity we are using the measuring
instrument and this measuring instrument
it is going to give us a value or a
reading okay and suppose this reading of
the measuring instrument it is different
from the actual value of the unknown
quantity so the difference between the
actual value and the value which we are
getting from the measuring instrument
there will be some variation in the two
values so that difference is called the
variation between the values suppose
like if we have to measure that how many
apples are there on the dining table
suppose the actual value of the apples
or actual number of apples is five okay
five apples are kept on the dining table
so when they are measuring a small
quantity then it may be possible that we
can actually count the numbers because
this is a very small number five apples
so we can correctly count the number of
apples suppose we have to measure or we
have to count 1500 afternoons now 1500
apples it is a big amount okay so it may
be possible that we were not able to
count the actual numbers okay so we will
give our results in the form that we
have counted 1500 apples but it may be
possible that hundred apples are also
more than it or hundred apples can be
less than it okay so whenever we define
our result in this form then we say that
some variation may be possible or we can
say some error has occurred in the
counting of the happens okay so we can
define this variation as the difference
between the two reading
again taking the same examples of 1500
apples suppose there are two observers
what is a and one is B when a is
counting the 1500 apples he is counting
at it does 1400 and B when B is counting
suppose he is counting at it does 1600
apples there is another observer who is
counting it as exactly the 1500 so we
are getting the values in the range from
1,500 1,600 1,400 so we can define it as
1500 plus minus 100 apples so this
difference between the two readings
which we are getting from different
observers or from the same observer also
so that difference is called the
variation now another word for this
variation or the uncertainty in the
measurement is error the technical term
which we give for this variation in the
readings or uncertainty in the readings
of the instrument is now
now error does not means that you have
got a wrong answer we cannot make that
error is same as that of mistake which
is done in the measurement because
mistake is that the bank they are doing
the measurement using a measuring
instrument at the time of measurement we
have done something wrong and you do
that we are getting the wrong reading so
that is called a mistake but error is
that we are getting a value which is
different from the actual value of the
unknown quantity okay so we can see that
error is a mathematical day
to show the uncertain ad in
measurement uncertainty means that they
are not sure they are not confirmed that
this is the actual value of the
measuring quantity okay so uncertain it
is that we are approximate so error is
like we have getting or we are giving an
approximate value that this can be the
value but we are not sure that this is
the actual value of the instrument okay
of that unknown quantity now let us
define the error in technical terms okay
so before defining it let me define two
terms true value and measured value true
value it is the known or the actual
value or the accepted value of the
unknown quantity and suppose the vane
machine it is giving us a different
value of that one kg of mass or one kg
of that object suppose we are getting
1.5 or 1.7 kg so that is the difference
between the actual value because actual
value is what 1 kg but we are getting
1.5 kg so that value which we are
getting from the weighing machine that
is called the measured value of that
object and the actual value and or the
true value of the weight of that object
is 1 kg so that is called the true value
which is known to us which is the
acceptable or the actual value so here
we can define the true value as the
known or actual or accepted value of the
quantity
Paris measured value it is the result
of an individual measurement of the
quantity means when the individual is
measuring that quantity with the help of
a measuring instrument so the result of
that measuring instrument or the reading
of that measuring instrument is called
the measured value so here are told that
the error it is the difference between
the two readings which we are getting so
here error will be defined as the
difference between the true value and
the measured value because true value is
the actual value of the quantity and
measured value is the value of the
quantity which we are getting after the
measurement so technically we can define
the error as the
so if he'll write the formula for it so
error is equal to measured value minus
the true value
so suppose we are measuring a resistance
and for that we are using a multimeter
and we know that the actual value of
that resistance is 98 herbs so true
value is 98 ohms but when we are
measuring that resistance using the
multimeter we are getting the reading
from the multimeter as hundred ohms so
the difference between the two readings
that is measured value and the true
value that will be the error so your the
error will be 100 minus 98 that is 2 so
2 is the error in the measurement so we
can defining we can define the error as
the difference between the measured
value and the true value
so if we talk about the error what we
are doing we are when we are doing the
measurement of an unknown quantity we
are getting the value and we are stating
that what is the difference between the
value which we are getting after the
measurement and what between the actual
value of that quantity so error we can
say that it gives a quantitative way
because we are giving a number to that
error that we are defining that the
difference between the actual value of
the resistance and the measured value is
to 2 ohms
so we are giving a quantity to that the
that what is the difference between or
what is the difference or what is the
confidence level of our measurement okay
so that is the error so also we can
define this error as the difference
between the instrument reading
okay now this arrow can also be
expressed in the form of percentage
arrow so percentage error will be
instrument reading minus the true
reading divided by the true reading
multiplied with 100 so we are defining
it in the form of percentage
so we can define or we can express the
errors in the measuring instrument in
the form of error also that is the
difference in the form of percentage
error also okay so in this video we
study that what is an error in the
measurement we see that the error is
defined as the difference between the
measured value that is the value which
is measured by the instrument divide
minus the true value of the unknown
quantity okay so I hope that this topic
is clear to you thank you
