In the figure let us assume the voltmeter to be ideal (internal resistance Rin=infinite).
So current Iv=0A
I= IA+IV
I=IA [IV=0A]
V=VA+VK
V=I×RA+I×Runknown
Ammeter is not ideal here.
V=I(RA+ Runknown)
V/I= RA+ Runknown [V/I= Measured value of resistance]
RM=RA+ Runknown
So the measured value of resistance is greater than the unknown value of resistance exceed by the value of RA.
Error calculation-
e= Rknown-Rm/ Rknown
or e=RA/ Rknown
If R ≅0, then Rm= Rknown (e ≈0)
I=IV+IK
I=V/RV+V/RK
I=V(1/RV+1/RK)
I/V=(1/RV+1/RK)
I/RM=I/RV+I/RK
I/RM=RV+ Rknown/RV Rknown
RM= RV Rknown/ RV+ Rknown
If the voltmeter is not ideal then measured value is Rknown.
Also Read-Wheatstone bridge
Also Read- Method of substitution