Question

To measure a potential difference across a resistor of resistance R a voltmeter of resistance $R_v$ is used. To measure the potential with a minimum accuracy of 95 % then

• A. $R_v$ = 5R
• B. $R_v$ = 15R
• C. $R_v$ = 10R
• D. $R_v$ > 19R

Answer 1

The correct option is D $R_v$ > 19R

According to figure 1, voltage across Resistance R is $v_0=iR$

Considering voltmeter of resistance $R_v$ ,voltmeter reading will be v.

$v=i\left(R||R_v\right)$

$=i\frac{R{R}_v}{R{+}_v}$

Accuracy should be 95% then we have,

$v>0.95v_0$

$i\frac{R{R}_v}{R+R_v}>0.95\left(iR\right)$

$R_v>0.95R+0.95R_v$

$0.05R_v>0.95R$

$R_v>\frac{0.95}{0.05}R$

$R_v>19R$