The actual value of resistance R, shown in the figure is `30 Omega`. This is measured in an experiment as shown using the standard formula `R = (V)/(I)`, where V and I are the readings of the voltmeter and ammeter, respectively. If the measured value of R is 5% less, then the internal resistance of the voltmeter is

Options

A. `35 Omega`
B. `600 Omega`
C. `570 Omega`
D. `350 Omega`

Answer

C

Explanation

Let the measured voltage be `V_(m)` and
Let the measured current be `i_(m)` and Let the ammeter be ideal, thus
`V_(m)/i_(m) = R_(m)`

`therefore (i_(1)R)/i_(m) = R_(m)`
`therefore R(R_(y)/(R + R_(v))) = R_(m)`
`therefore 1/R_(m) = 1/R + 1/R_(v)`
`therefore 1/R_(v) = 1/R_(m) -1/R =1/(0.95 R) -1/R`
`therefore 1/R_(v) =1/R (1-0.95)/0.95`
`therefore R_(v) = 19 R`
`rArr R_( v) = 570 Omega`