A DArsonval moving coil voltmeter with an internal resistanc

A D’Arsonval moving coil voltmeter with an internal resistance of 100 is set to a range of 10V. This voltmeter is connected to a circuit and gives a reading of 5V. This reading is checked with a recently calibrated voltmeter which gives a reading of 5.5V. The implication is that the first voltmeter has an incorrect resistance in series. The meter deflects full scale when 1mA current flows through it. Calculate: (i) The value of the correct series resistance for the 10V range. (ii) The value of the incorrect series resistance.

Solution

Internal Resistance of Meter Ri=100 ohms

Full scale deflection current I_fsd=1mA

(i) V=I(R_se+R_i) where Rse is series Resistance

as V=10 V I=I_fsd=1mA

R_se+R_i=V/I=10/1m=10000 ohms

R_se=10000-R_i=9900 ohms

so correct value of series resistance to be connected is R_se=9900 ohms

(ii) For Voltage value of 5.5 V ,meter reading only 5 V

Current required for 5 V reading is I= I_fsd*5/10 =0.5 mA

But actual voltage applied is 5.5 V

so I= 5.5/(R_i+R_se(incorrect))=0.5 mA

R_i+R_se(incorrect)=5.5/0.5 m=11000 ohms

R_se(incorrect)=11000-R_i=10900 ohms

so incorrect values of series resistance is R_se(incorrect)=10900 ohms