Question
When a current of $$5 mA$$ is passed through a galvanometer having a coil of resistance $$15\,\Omega $$ it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into to voltmeter of range $$0 - 10 V$$ is
A.
$$2.535 \times {10^3}\Omega $$
B.
$$4.005 \times {10^3}\Omega $$
C.
$$1.985 \times {10^3}\Omega $$
D.
$$2.045 \times {10^3}\Omega $$
Answer :
$$1.985 \times {10^3}\Omega $$
Solution :
Given : Current through the galvanometer,
$${i_g} = 5 \times {10^{ - 3}}A$$
Galvanometer resistance, $$G = 15\,\Omega $$
Let resistance $$R$$ to be put in series with the galvanometer to convert it into a voltmeter.
$$\eqalign{
& V = {i_g}\left( {R + G} \right) \cr
& 10 = 5 \times {10^{ - 3}}\left( {R + 15} \right) \cr
& \therefore R = 2000 - 15 = 1985 \cr
& = 1.985 \times {10^3}\,\Omega \cr} $$