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  • The galvanometer Q has internal resistance  and full scale defl

The galvanometer Q has internal resistance \mathrm{Q=50\, \Omega} and full scale deflection occurs at \mathrm{i=1 \mathrm{~mA}}.Find the series resistor \mathrm{R_{3}} needed to use the arrangement as a voltmeter with different range as shown in the figure.  



 

Option: 1

9 \, \mathrm{k} \Omega


Option: 2

90\, \mathrm{k} \Omega


Option: 3

18 \, \mathrm{k} \Omega


Option: 4

30


Answers (1)

best_answer

For the range of \mathrm{V_{1}=1} volt
\mathrm{i_{g}=\frac{V_{1}}{Q+R_{1}} \text { or } 10^{-3}=\frac{1}{50+R_{1}}}.
\mathrm{\text { or } R_{1}=1000-50 \, \Omega=950\, \Omega}

For the range of \mathrm{V_{2}=10 \mathrm{~V}}
\mathrm{i_{g}=\frac{V_{2}}{Q+R_{1}+R_{2}} \text { or } 10^{-3}=\frac{10}{50+950+R_{2}} }
\mathrm{\text { or } R_{2}=900\, \Omega=9\, \mathrm{k} \Omega}

For the range of \mathrm{V_{3}=100 \mathrm{~V}}
\mathrm{i_{g}=\frac{V_{3}}{Q+R_{1}+R_{2}+R_{3}} \Rightarrow 10^{-3}=\frac{100}{ 50+950+9000+R_{3}}}
\mathrm{\Rightarrow R_{3}=90,000 \, \Omega=90\, \mathrm{k} \Omega}
 

Posted by

rishi.raj

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