Question

The percentage error in measuring the voltage across a resistor 'r' by a voltmeter of resistance 'R'(current assumed to be constant) is?

Answer 1

From figure we can say, $V=(i-i_g)r$

Value of current will be, $i_g=I\times \frac{r}{R+r}$

Voltage across voltmeter, $V_m=\frac{IRr}{R+r}$

For ideal voltmeter, $V_i=Ir$

So, error will be, $=\frac{V_m-V_i}{V_m}\times 100=\frac{\frac{IrR}{R+r}-Ir}{\frac{IrR}{R+r}}\times 100$

$=\frac{R}{r+R}-1=-\frac{r}{R+r}\times 100$