In Ohm's experiment, the value of an unkn | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

${\rm{(i)}}\,\,{\rm{\bar R}}\, = \frac{{{{\rm{R}}_{\rm{1}}}\, + {{\rm{R}}_{\rm{2}}}\, + {{\rm{R}}_{{\rm{3}}\,\,}} + {{\rm{R}}_{\rm{4}}}}}{{\rm{4}}}$

Vedclass · Accepted Answer

$0.04, 0.0096$

Vedclass · Answer

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

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.

Similar Questions

Write a note on combination of error.

The temperature of a metal coin is increased by $100^{\circ} C$ and its diameter increases by $0.15 \%$. Its area increases by nearly

The percentage errors in the measurement of mass and speed are $2\%$ and $3\%$ respectively. How much will be the maximum error in the estimation of the kinetic energy obtained by measuring mass and speed ......... $\%$