Question

The resistance of a galvanometer is 10Ω. It gives full-scale deflection when 1 mA current is passed. The resistance connected in series for converting it into a voltmeter of 2.5 V will be.
A. 24.9 Ω
B. 249 Ω
C. 2490 Ω
D. 24900 Ω

Answer 1

Hint: A galvanometer is an electromechanical instrument used for detecting and indicating an electric current. A galvanometer works as an actuator, by producing a rotary deflection (of a "pointer"), in response to electric current flowing through a coil in a constant magnetic field.

Complete step by step solution:
Let G is Resistance of a galvanometer and that is equals to 10Ω.
i.e. \[G = 10\Omega \]
($i_g$) be the current through the galvanometer for full scale deflection its value i.e.
\[{i_g} = 1{\text{ }}mA\]
Now, to convert a galvanometer into a voltmeter a large resistance should be connected in series with the galvanometer.
Let resistance R is connected in series with galvanometer of resistance G
\[\therefore {R_{eq}} = G + R\], where Req is equivalent to a galvanometer.
Hence, current through the circuit is (current passing through a circuit is defined as ratio between potential difference in the circuit to the equivalent resistance )

\[{i_g} = \dfrac{v}{{G + R}}\], where \[v\] is voltage of voltmeter
Now putting the value of G and R we get the following expression
\[{10^{ - 3}} = \dfrac{{2.5}}{{10 + R}}\]
By solving the above expression we get the value of resistance connected in series with voltmeter i.e. R
Hence, \[R = 2490\Omega \]

Therefore option C is Correct.

Note: Be careful about all the units and scales which are given. Firstly try to convert all in the CGS system of the unit and then solve it. In this question Resistance of a galvanometer is given to us that is G.