Question

A voltmeter reads 5.0 V at full-scale deflection and is graded according to its resistance per volt at full-scale deflection as $5000\Omega V^{-1}$. How will you convert it into a voltmeter that reads 20 V at full-scale deflection? Will it still be graded as 5000 $\Omega V^{-1}$? Will you prefer this voltmeter to one that is graded $2000\Omega V^{-1}$?

Answer 1

Let $R$ be the voltmeter resistance,
If the voltmeter has to read 20V at full scale deflection, we need an additional resistance r in series with it. Thus
$\frac{5}{R}=\frac{20}{R+r}$...........(1)
since the voltmeter is graded as 5000 ohms/V for full scale deflection of 5V.
$R=5000\times 5$
From (1)
$\frac{1}{5000}=\frac{20}{25000+r}$
$r=75000$ ohms