Page 41 - Class-11-Physics-Part-1_Neat

UNITS AND MEASUREMENT 27

Then,
Example 2.9 The resistance R = V/I where ∆Z/Z = (∆A/A) + (∆A/A) = 2 (∆A/A).
t
V = (100 ± 5)V and I = (10 ± 0.2)A. Find the Hence, the relative error in A is two times the
2
percentage error in R.
error in A.
Answer The percentage error in V is 5% and in In general, if Z = A B /C r
q
p
I it is 2%. The total error in R would therefore Then,
be 5% + 2% = 7%. t ∆Z/Z = p (∆A/A) + q (∆B/B) + r (∆C/C).
Example 2.10 Two resistors of resistances Hence the rule : The relative error in a
t
R = 100 ±3 ohm and R = 200 ± 4 ohm are physical quantity raised to the power k is the
2
1
connected (a) in series, (b) in parallel. Find k times the relative error in the individual
the equivalent resistance of the (a) series quantity.
combination, (b) parallel combination. Use
for (a) the relation R = R + R and for (b) t Example 2.11 Find the relative error in
1 2,
Z, if Z = A B 1/3 /CD 3/2 .
4
and
Answer The relative error in Z is ∆Z/Z =
Answer (a) The equivalent resistance of series 4(∆A/A) +(1/3) (∆B/B) + (∆C/C) + (3/2) (∆D/D).
combination t
R = R + R = (100 ± 3) ohm + (200 ± 4) ohm
1 2 t Example 2.12 The period of oscillation of
= 300 ± 7 ohm. a simple pendulum is T = 2π L/g.
(b) The equivalent resistance of parallel Measured value of L is 20.0 cm known to 1
combination mm accuracy and time for 100 oscillations
R R 200 of the pendulum is found to be 90 s using
R′= 1 2 = = 66.7 ohm a wrist watch of 1 s resolution. What is the
R + R 3
1 2 accuracy in the determination of g ?
1 1 1 2 2
Then, from R′ = R 1 + R 2 Answer g = 4π L/T t ∆ ∆ t ∆
t
we get, Here, T = n and T∆ = n . Therefore, T T = t .
∆ R′ = ∆ R 1 + ∆ R 2 The errors in both L and t are the least count
R′ 2 R 2 R 2 errors. Therefore,
2
1
(∆g/g) = (∆L/L) + 2(∆T/T )
)
)
.
∆ R′ = ( R′ 2 ∆ R 1 + ( R′ 2 ∆ R 2 0 1  1 
.
R 1 2 R 2 2 = 20 0 + 2   90  = 0 027
.
 66.7  2  66.7  2 Thus, the percentage error in g is
=
  3 +   4 100 (∆g/g) = 100(∆L/L) + 2 × 100 (∆T/T )
 100   200 
= 3% t
= 1.8
2.7 SIGNIFICANT FIGURES
±
Then, R′ = 66.7 1.8 ohm
(Here, ∆R is expresed as 1.8 instead of 2 to As discussed above, every measurement
keep in confirmity with the rules of significant involves errors. Thus, the result of
figures.) t measurement should be reported in a way that
indicates the precision of measurement.
Normally, the reported result of measurement
(c) Error in case of a measured quantity is a number that includes all digits in the
raised to a power
number that are known reliably plus the first
Suppose Z = A , digit that is uncertain. The reliable digits plus
2

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