The current in a conductor and the potential difference across its ends are measured by an ammeter and a voltmeter. The meters draw negligible currents. The ammeter is accurate but the voltmeter has a zero error (that is, it does not read zero when no potential difference is applied). Calculate the zero error if the readings for two different conditions are 1.75 A, 14.4 V and 2.75 A, 22.4 V.
0.4V
Given,
Ammeter reading of current, i1 in the 1st case=1.75A
Ammeter reading of current, i2 in the 2nd case=2.75A
Voltmeter reading for current i1, V1=14.4V
Voltmeter reading for current i2, V2=22.4V
Formula used
The ammeter shows the accurate reading while the voltmeter deviate from showing the corresponding potential difference value due to the presence of Zero error, Ve.
Hence the original potential difference can be calculated as, Vo
Where V is the shown voltage in the defected voltmeter.
We also know that the potential difference across the conductor is, V
Where R is the resistance of the conductor
Solution:
For the 1st and 2nd case, the relation between absolute current and voltage can be written, from eqn.2, as
And
By dividing these expressions, we get
The terms Vo1 and Vo2 in above equation can be replaced by eqn.1 as
By substituting the given values in the above expression, we get
Or,
Or,
Or,
Or,
Hence the zero error associated with the measurement is 0.4V.