Question

A galvanometer having a coil resistance $100\Omega$ gives a full scale deflection when a current of $1mA$ is passed through it. What is the value of the resistance which can convert this galvanometer into voltmeter giving full scale deflection for a potential difference of $10V$? Resistance required in series to convert it into voltmeter of range $10$ .

• A. $7.9K\Omega$
• B. $8.9K\Omega$
• C. $9.9K\Omega$
• D. $10K\Omega$

Answer 1

The correct option is C

$9.9K\Omega$

Step 1. Given data:

Current flowing through Galvanometer , $I_g=1mA$

$\therefore I_g=1\times {10}^{-3}A$

Resistance of Galvanometer, $R_g=100\Omega$

Potential difference, $V_A-V_B=10v$

Required Resistance, $R$

Step 2. Calculating Required resistance, $R$ :

Applying Kirchhoff's law between A and B.

$V_A-I_g{R}_g-I_{g}R=V_B$
$\begin{array}{rcl}& \Rightarrow & V_A-V_B=I_g{R}_g+I_{g}R\\ & \Rightarrow & 10=I_g\left(R_g+R\right)\\ & \Rightarrow & 10={10}^{-3}\left(100+R\right)\\ & \Rightarrow & {10}^4=100+R\\ & \Rightarrow & R=9900\Omega \\ \therefore R& =& 9.9K\Omega \end{array}$

Hence, correct option is (C).