Voltmeter-Ammeter method for measurement of medium resistance

In the figure let us assume the voltmeter to be ideal (internal resistance R_in=infinite).

So current Iv=0A

I= I_A+I_V

I=I_A       [I_V=0A]

V=V_A+V_K

V=I×R_A+I×R_unknown

Ammeter is  not ideal here.

V=I(R_A+ R_unknown)

V/I= R_A+ R_unknown            [V/I= Measured value of resistance]

R_M=R_A+ R_unknown

So the measured value of resistance is greater than the unknown value of resistance exceed by the value of R_A.

Error calculation-

e= R_known-R_m/ R_known

or        e=R_A/ R_known

If R ≅0, then Rm= R_known (e ≈0)

I=I_V+I_K

I=V/R_V+V/R_K

I=V(1/R_V+1/R_K)

I/V=(1/R_V+1/R_K)

I/RM=I/RV+I/RK

I/RM=RV+ R_known/RV R_known

RM= RV R_known/ RV+ R_known

If the voltmeter is not ideal then measured value is R_known.

Also Read-Wheatstone bridge

Also Read- Method of substitution