A voltmeter gives readings that are larger than the true values and has a systematic error that varies with voltage.

Question 12

A voltmeter gives readings that are larger than the true values and has a systematic error that varies with voltage.

Which graph shows the calibration curve for the voltmeter?

Reference: Past Exam Paper – November 2016 Paper 11 & 13 Q4

Solution:

Answer: A.

The voltmeter has a systematic error in that the reading it gives it always greater than the true values.

If the true value is zero, the voltmeter would give a value greater than zero. Thus, the curve CANNOT pass through the origin (0,0) as this would indicate that the reading is the same as the true value, and not greater. [C is incorrect]

Graph D shows that when the meter reading is 0 V, the true value is greater than 0 V. This indicates that the true value is greater than the meter reading. But the questions tells us that it is the voltmeter reading which is greater than the true value. [D is incorrect]

So, when the true value is zero, the meter would give a reading greater than zero. Both graphs A and B contains this information.

We are also told that the systematic error varies with voltage. That is, for example (random values are given),

When true value = 0 V, meter reading = 0.5 V (this is 0.5 greater)

When true value = 1 V, meter reading = 1.7 V (this is 0.7 greater)

So, the amount by which the meter reading is greater than the true value changes.

Graph B shows a constant systematic error (the difference between the meter reading and the true value is constant). The meter reading is always greater by the same amount. [B is incorrect]

Graph A is correct, because the difference between the meter reading and the true value increases with voltage.

Graphs C and D both show varying systematic errors but the meter readings are smaller than the true values.