Advertisements
Advertisements
प्रश्न
In Ohm’s experiments, the values of the unknown resistances were found to be 6.12 Ω, 6.09 Ω, 6.22 Ω, 6.15 Ω. Calculate the (mean) absolute error, relative error, and percentage error in these measurements.
Advertisements
उत्तर
Given: a1 = 6.12 Ω, a2 = 6.09 Ω, a3 = 6.22 Ω, a4 = 6.15 Ω
To find:
i. Absolute error `(Δ"a"_"mean")`
ii. Relative error
iii. Percentage error
Formulae:
1. `"a"_"mean" = ("a"_1 + "a"_2 + "a"_3 + "a"_4)/4`
2. `Delta"a"_"n" = |"a"_"mean" - Delta"a"|`
3. `Delta"a"_"mean" = (Delta"a"_1 + Delta"a"_2 + Delta"a"_3 + Delta"a"_4)/4`
4. Relative error = `(Delta"a"_"mean")/"a"_"mean"`
5. Percentage error = `(Delta"a"_"mean")/"a"_"mean" xx 100%`
Calculation: From formula (i),
`"a"_"mean" = (6.12 + 6.09 + 6.22 + 6.15)/4`
`= 24.58/4 = 6.145` Ω
From formula (ii),
`Delta"a"_1 = |6.145 - 6.12| = 0.025`
`Delta"a"_2 = |6.145 - 6.09| = 0.055`
`Delta"a"_3 = |6.145 - 6.22| = 0.075`
`Delta"a"_4 = |6.145 - 6.15| = 0.005`
From formula (iii),
`Delta"a"_"mean" = (0.025 + 0.055 + 0.075 + 0.005)/4`
`= 0.160/4`
= 0.04 Ω
From formula (iv),
Relative error =`0.04/6.145 = 0.0065` Ω
From formula (v),
Percentage error = 0.0065 × 100 = 0.65%
- The mean absolute error is 0.04 Ω.
- The relative error is 0.0065 Ω.
- The percentage error is 0.65%.
APPEARS IN
संबंधित प्रश्न
The error in the measurement of the sides of a rectangle is 1%. The error in the measurement of its area is ______.
Define absolute error.
If the measured values of the two quantities are A ± ΔA and B ± ΔB, ΔA and ΔB being the mean absolute errors. What is the maximum possible error in A ± B? Show that if Z = `"A"/"B"`
`(Delta "Z")/"Z" = (Delta "A")/"A" + (Delta "B")/"B"`
Answer the following question.
Show that if Z = `"A"/"B"`, `(triangle"Z")/"Z" = (triangle"A")/"A" + (triangle "B")/"B"`
In a workshop, a worker measures the length of a steel plate with Vernier calipers having a least count 0.01 cm. Four such measurements of the length yielded the following values: 3.11 cm, 3.13 cm, 3.14 cm, 3.14 cm. Find the mean length, the mean absolute error, and the percentage error in the measured value of the length.
Solve the numerical example.
If the formula for a physical quantity is X = `("a"^4"b"^3)/("c"^(1//3)"d"^(1//2))` and if the percentage error in the measurements of a, b, c and d are 2%, 3%, 3% and 4% respectively. Calculate percentage error in X.
In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where X = `(A^2B^(1/2))/(C^(1/3)D^3)`, will be:
Measure of two quantities along with the precision of respective measuring instrument is A = 2.5 ms–1 ± 0.5 ms–1 B = 0.10 s ± 0.01 s. The value of A B will be ______.
You measure two quantities as A = 1.0 m ± 0.2 m, B = 2.0 m ± 0.2 m. We should report correct value for `sqrt(AB)` as ______.
Time for 20 oscillations of a pendulum is measured as t1 = 39.6 s; t2 = 39.9 s; t3 = 39.5 s. What is the precision in the measurements? What is the accuracy of the measurement?
The resistance R = `"V"/"I"`, where V = (50 ± 2) V and I = (20 ± 0.2)A. The percentage error in R is 'x' %.
The value of x to the nearest integer is ______.
If E, L, M, and G denote the quantities as energy, angular momentum, mass, and constant of gravitation respectively, then the dimensions of P in the formula P = EL2M−5G−2 are ______.
The dependence of g on geographical latitude at sea level is given by `g = g_0(1 + betasin^2Phi)` where Φ is the latitude angle and β is a dimensionless constant. If Δg is the error in the measurement of g then the error in measurement of latitude angle is ______.
A travelling microscope has 20 divisions per cm on the main scale while its Vernier scale has total 50 divisions and 25 Vernier scale divisions are equal to 24 main scale divisions, what is the least count of the travelling microscope?
A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in 1 cm on main scale and 50 Vernier scale divisions are equal to 49 main scale divisions, then least count of the travelling microscope is ______ × 10-6 m.
A thermometer always reads 2°C higher than the actual temperature because its zero mark is incorrect. What type of error is this?
A laboratory balance shows a mass reading even when no object is placed on the pan. What is the main cause of this error?
A weighing scale that always reads a constant +0.2 kg because its zero mark is misaligned is a clear example of a(n):
A student reads a measuring cylinder from above the liquid level, causing the reading to be higher than the actual value. What type of error is this?
Which one of the following is an effective way to reduce systematic errors in an experiment?
If the pointer of the voltmeter is not exactly at the zero of the scale, then the error is called ______.
Instrumental error can be minimised by ______.
Constant error can be caused due to ______.
