Question

A galvanometer has a coil of resistance 100 ohm and gives a full scale deflection for 30 mA current. If it is to work as a voltmeter of 30 volt range, the resistance required to be added will be

$$A.{\text{ }}1000\Omega \\\ B.{\text{ }}900\Omega \\\ C.{\text{ }}1800\Omega \\\ D.{\text{ }}500\Omega \\\$$

Answer 1

- Hint: In order to deal with this question we will use the concept to convert the galvanometer into a voltmeter of a given range by connecting a resistance R in series of appropriate resistance according to the problem. Further we will use the formula to find the value of R which is mentioned in solution to get the required answer.

Formula used- $V = {I_g}\left( {G + R} \right)$

Complete step-by-step solution -

Given that
Resistance of galvanometer, $G = 100Q$
Current for full scale deflection:
${I_g} = 30mA = 30 \times {10^{ - 3}}A$
Range of voltmeter, $V = 30V$
To convert the galvanometer into a voltmeter of a given range, a resistance R is connected in series with it as shown in the figure.

From the above figure the voltage V across the points is:
$V = {I_g}\left( {G + R} \right)$
The above equation can be written as:

$$\because V = {I_g}\left( {G + R} \right) \\\ \Rightarrow G + R = \dfrac{V}{{{I_g}}} \\\ \Rightarrow R = \dfrac{V}{{{I_g}}} - G \\\$$

Substitute the given values in above formula we have

$$\because R = \dfrac{V}{{{I_g}}} - G \\\ \Rightarrow R = \dfrac{{30}}{{30 \times {{10}^{ - 3}}}} - 100\Omega \\\ \Rightarrow R = 1000\Omega - 100\Omega \\\ \Rightarrow R = 900\Omega \\\$$

Hence, the resistance required to be added will be $900\Omega$
So, the correct answer is option B.

Note- A galvanometer is an electromechanical device which is used to measure and signify electrical current. A galvanometer acts as an actuator in response to electrical current flowing through a coil in a continuous magnetic field, by generating a rotary deflection (of a "pointer"). Galvanometer is an instrument which is used by deflection of a moving coil to measure a specific electrical current or a current operation. The deflection is a mechanical rotation which is derived from the current forces.