Question

A voltmeter has internal resistance $r\Omega$ and range $V$ volts. The value of resistance used in series to convert it into a voltmeter of range $4V$ volts is:

• A. $4r$
• B. $\frac{r}{4}$
• C. $3r$
• D. $\frac{r}{3}$

Answer 1

Answer: (C)

$3r$

$\frac{V_1}{V_2}=\frac{R_1}{R_2}$ Since $V=iR$ and $i$ is constant in series combination.
$\frac{V_1}{V_2}=\frac{R_1}{R_2}\Rightarrow \frac{V}{4V}=\frac{r}{r+x}$
$\Rightarrow$ $r+x=4r$
$\Rightarrow$ $x=3r$