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A voltmeter of resistance RV and an amme...

A voltmeter of resistance `R_V` and an ammeter of resistance `R_A` are connected in a circuit to measure a resistance R as shown in figure. The ratio of the meter readings gives an apparent resistance `R^'`. Show that R and `R^'` are related by the relation
`1/R=1/R^'-1/R_V`

Text Solution

Verified by Experts

Apparent resistance,
`R^'=("voltmeter reading")/("ammeter reading")=V/I`
Total resistance of circuit, `R_(eq)=R_A+(R R_V)/(R+R_V)`
According to Ohm's law, `epsilon/I=R_A+(R R_V)/(R+R_V)`
Also, `epsilon=IR_A+V` or `epsilon/I=R_A+V/I=R_A+R^'`
or `R_A=(R R_V)/(R+R_V)=R_A+R^'` or `R^'=(R R_V)/(R+R_V)`
or `1/R^'=(R+R_V)/(R R_V)=1/R_V+1/R`
or `1/R=1/R^'-1/R_V`
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