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Resistance value of an unknown resistor ...

Resistance value of an unknown resistor is calculated using the formula `R=V/I` where V and I be the readings of the voltmeter and the ammeter respectively. Consider the circuits below. The internal resistances of the voltmeter and the ammeter (`R_v and R_G `respectively ) are finite and non zero.

Let `R_v and R_G` be the calculated values in the two cases A and B respectively.
If the resistance of voltmeter is `R_v=1kOmega` and that of ammeter is `R_G=1Omega` the magnitude of the percentage error in the measurement of R (the value of R is nearly `10Omega` ) is:

A

zero in both cases

B

non zero but equal in both cases

C

more in circuit A

D

more in circuit B

Text Solution

Verified by Experts

% error in case A=`(R_A-R)/R times 100%=(R_v/(R+R_v)-1) times 100% = (-R)/(R+R_v) times 100% approx -1%`
% error in case B =`(R_0-R)/R times 100%=R_g/R times 100% approx 10%`
Hence percentage error in circuit B is more than that in A.
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