Question

A voltmeter of variable ranges $3V,15V,150V$ is to be designed by connecting resistances $R_1,R_2,R_3$ in series with a galvanometer of resistance $G=20\Omega$ , as shown in the figure. The galvanometer gives full pass through its coil. Then, the resistances $R_1,R_2$ and $R_3$ (in kilo ohms) should be, respectively

• A. $3,12,135$
• B. $2.98,12,135$
• C. $2.98,14.98,149.98$
• D. $3.86,12.55,122.97$

Answer 1

Answer: (B)

$R=\frac{V}{I_g}-R_g$
$R_1=\frac{3}{I_g}-R_g=2980\Omega =2.98k\Omega$
$\left(R_1+R_2\right)=\frac{15}{I_g}-Rg=14980\Omega =14.98k\Omega$
$\left(R_1+R_2+R_3\right)=\frac{150}{I_g}-R_g=149980\Omega$
$=149.98k\Omega$
$\Rightarrow R_1=2.98k\Omega$
$R_2=14.98-2.98=12k\Omega$
$R_3=149.98-14.98=135k\Omega$