A galvanometer of resistance 100\Omega has 50 divisions on its scale and has sensitivity of 20 \mu A/ division. It is to be converted to a voltmeter with three ranges, of 0-2V0-10V and 0-20V. The appropriate circuit to do so is :

  • Option 1)

    R_{1}=2000\Omega

                                              R_{2}=8000\Omega

                                              R_{3}=10000\Omega

     

  • Option 2)

    R_{1}=19900\Omega

                                             R_{2}=9900\Omega

                                             R_{3}=1900\Omega                                                                                            

  • Option 3)

    R_{1}=1900

                                              R_{2}=8000

                                              R_{3}=10000

  • Option 4)

     R_{1}=1900

                                               R_{2}=9900

                                                R_{3}=19900

 

Answers (1)

 

Conversion of galvanometer into voltameter -

Connected a large Resistance R  in series

- wherein

 

 

Ig =50\times20=1mA

option (2) can not ever be appropriate circuit because we can not measure high voltage i.e 20V before smaller voltage i.e 2V, because if the higher voltage is at the end then the resistance is large and hence more range.

Now checking option (1), (2), & (3)

Ig(100+R_{1})=2V

100+R_{1}=2\times10^{3}

\Rightarrow R_{1}=1900\Omega ...................option (1) is false 

\Rightarrow Ig (100+R_{1}+R_{2})=10V

\Rightarrow R_{2}=10000-100-1900

R_{2}=8000

\Rightarrow Ig(100+R_{1}+R_{2}+R_{3})=20V

R_{3}=20000-8000-1900-100

R_{3}=10000\Omega


Option 1)

R_{1}=2000\Omega

                                          R_{2}=8000\Omega

                                          R_{3}=10000\Omega

 

Option 2)

R_{1}=19900\Omega

                                         R_{2}=9900\Omega

                                         R_{3}=1900\Omega                                                                                            

Option 3)

R_{1}=1900

                                          R_{2}=8000

                                          R_{3}=10000

Option 4)

 R_{1}=1900

                                           R_{2}=9900

                                            R_{3}=19900

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