Question

a voltmeter v of 23 k ohm resistance in series with a resistor r across a 230v supply reads 92v. calculate the value of the resistor r 

Answer 1

Given :

Resistance of Voltmeter$=R$_V$=23k$$\Omega$

Reading of voltmeter = Potential difference across the voltmeter $=92V$

External source is applied of voltage $=230V$

So Potential difference across resistance r will be $= 230V-92V= 138V$

To calculate the value of resistance r

from Diagram

Current through the voltmeter and resistance r will be

$I= \frac{230V}{R_v + r}$ by Ohm's Law

Now potential difference across voltmeter = reading of voltmeter $=92V$ $= IR_v$ $= \frac{230R_V}{R_v+r}$

after putting value of $R$_v

$\implies$ $\frac{r}{R_v} = \frac{230}{92}-1$

$\implies r = 1.5 \times R_v$ = $34500\Omega$

Final answer

The value of resistance r connected in series with voltmeter is $34.5k\Omega$ .