In Ohm's experiment to measure resistance different observation of unknown resistance are 4.12ohm, 4.08ohm,4.22ohmand 4.14ohm .Find average absolute error, relative error and percentage error.
Answers
Answer:
Absolute error = 0.02, 0.06, 0.08 and 0.00
Relative error = 9.66 \times 10^{-3}9.66×10
−3
Percentage errror = 9.67%
Explanation:
Absolute error: It is defined as difference between mean value and given individual value.
Given R₁=4.12, R₂=4.08, R₃=4.22,R₄=4.14
Mean value of all resistance=
R_{mean}R
mean
=(R₁+R₂+R₃+R₄)/4=(4.12+4.08+4.22+4.14)/4
R_{mean}=4.14R
mean
=4.14
Absolute error,
ΔR₁= R_{mean}-R_{1}R
mean
−R
1
=4.14-4.12=0.02
ΔR₂= R_{mean}-R_{2}R
mean
−R
2
=4.14-4.08=0.06
ΔR₃= R_{mean}-R_{3}R
mean
−R
3
=4.14-4.22=0.08
ΔR₄= R_{mean}-R_{4}R
mean
−R
4
=4.14-4.14=0.00
Relative error:It is the ratio of absolute mean error and given individual mean value.
ΔR_{mean}R
mean
=(0.02+0.06+0.08+0.00)/4=0.04
Relative error = ΔR_{mean}R
mean
/R_{mean}R
mean
=0.04/4.14=9.66\times10^{-3}9.66×10
−3
Percentage error = when relative error is expressed in terms of percentage then percentage error is defined.
Percentage error = (ΔR_{mean}R
mean
/R_{mean}R
mean
)*100
\frac{0.04}{4.14} \times100
4.14
0.04
×100 =9.67%