In Ohm's experiment, the value of an unknown resistance were found to be 4.12; Omega, 4.08 ;Omega, 4.22 ;Omega and 4.14 ;Omega. Calculate absolute error

Q: In Ohm's experiment, the value of an unknown resistance were found to be $4.12\; \Omega, 4.08 \;\Omega, 4.22 \;\Omega$ and $4.14 \;\Omega$. Calculate absolute error and relative error in these measurement.

a ${\rm{(i)}}\,\,{\rm{\bar R}}\, = \frac{{{{\rm{R}}_{\rm{1}}}\, + {{\rm{R}}_{\rm{2}}}\, + {{\rm{R}}_{{\rm{3}}\,\,}} + {{\rm{R}}_{\rm{4}}}}}{{\rm{4}}}$ $\, = \,\,\frac{{{\rm{4}}{\rm{.12}} + {\rm{4}}{\rm{.08}} + {\rm{4}}{\rm{.22}} + {\rm{4}}{\rm{.14}}}}{{\rm{4}}}\,\, = \,\,\frac{{{\rm{16}}{\rm{.56}}}}{{\rm{4}}}\,\, = \,\,{\rm{4}}{\rm{.14}}$ ${\rm{\Delta }}{{\rm{R}}_{\rm{1}}}\, = \,{\rm{4}}{\rm{.14}} - \,{\rm{4}}{\rm{.12}}\, = \,{\rm{0}}{\rm{.02,}}$ $\,{\rm{\Delta }}{{\rm{R}}_{\rm{2}}}\, = {\rm{4}}{\rm{.14}}\, - {\rm{4}}{\rm{.08}}\, = \,{\rm{0}}{\rm{.06,}}\,$ $\,{\rm{\Delta }}{{\rm{R}}_{\rm{3}}}\, = {\rm{4}}{\rm{.14}}\, - {\rm{4}}{\rm{.22}}\, = \,{\rm{0}}{\rm{.08,}}\,$ ${\rm{\Delta }}{{\rm{R}}_{\rm{4}}} = \,{\rm{4}}{\rm{.14}}\, - \,{\rm{4}}{\rm{.14}}\, = \,{\rm{0}}{\rm{.00}}$ ${\rm{\Delta \bar R}}\,\, = \,\frac{{{\rm{|}}\,{\rm{\Delta }}{{\rm{R}}_{\rm{1}}}\,{\rm{|}}\, + \,{\rm{|}}\,{\rm{\Delta }}{{\rm{R}}_{\rm{2}}}\,{\rm{|}}\, + \,{\rm{|}}\,{\rm{\Delta }}{{\rm{R}}_{\rm{3}}}\,{\rm{|}}\, + \,{\rm{|}}\,{\rm{\Delta }}{{\rm{R}}_{\rm{4}}}\,{\rm{|}}}}{{\rm{4}}}\,\,\,$ $\, = \,\,\frac{{{\rm{|}}\,\,{\rm{0}}{\rm{.02|}} + {\rm{|0}}{\rm{.06|}} + {\rm{|}}\, - \,{\rm{0}}{\rm{.08}}\,{\rm{|}}\, + \,{\rm{|}}\,{\rm{0}}{\rm{.00}}\,{\rm{|}}}}{{\rm{4}}}$ $\, = \,\frac{{{\rm{0}}{\rm{.16}}}}{{\rm{4}}}\,\,\, = \,\,{\rm{0}}{\rm{.04}}$ absolute error $\Delta \bar R\,\, = \,\,0.04$ relative error $\frac{{{\rm{\Delta \bar R}}}}{{{\rm{\bar R}}}}\, = \,\frac{{{\rm{0}}{\rm{.04}}}}{{{\rm{4}}{\rm{.14}}}}\,\,\, = \,{\rm{0}}{\rm{.00966}}\,\, = \,\,\,{\rm{0}}{\rm{.0096}}$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

In Ohm's experiment, the value of an unknown resistance were found to be $4.12\; \Omega, 4.08 \;\Omega, 4.22 \;\Omega$ and $4.14 \;\Omega$. Calculate absolute error and relative error in these measurement.

A$0.04, 0.0096$
B$0.4, 0.096$
C$0.004, 0.96$
D$0.004, 0.00096$

Diffcult

STD 11 Science
JEE
STD 11 - 1. units,dimensions and measurement
Physics

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