Question
A microammeter has a resistance of $$100\,\Omega $$ and full scale range of $$50\,\mu A.$$ It can be used as a voltmeter or as a higher range ammeter provided a resistance is added to it. Pick the correct range and resistance combination
A.
$$50\,V$$ range with $$10\,k\Omega $$ resistance in series
B.
$$10\,V$$ range with $$200\,k\Omega $$ resistance in series
C.
$$10\,mA$$ range with $$1\,\Omega $$ resistance in parallel
D.
$$10\,mA$$ range with $$0.1\,\Omega $$ resistance in parallel
Answer :
$$10\,V$$ range with $$200\,k\Omega $$ resistance in series
Solution :
$$\eqalign{
& {i_g} = i\left( {\frac{{SG}}{{S + G}}} \right) \cr
& {\text{or}}\,\,50 \times {10^{ - 6}} = i\left( {\frac{S}{{S + 100}}} \right)\,......\left( {\text{i}} \right) \cr
& {\text{Also}}\,\,V = {i_g}\left( {G + {R_0}} \right) \cr
& {\text{or}}\,\,V = 50 \times {10^{ - 6}}\left( {100 + {R_0}} \right)\,......\left( {{\text{ii}}} \right) \cr} $$
On simplifying above equations, we get
$$V = 10\,V,{R_0} = 200 \times {10^{ - 3}}\,\Omega $$