Problema 16-6
Source:
Problem created by the author of the site.
A voltmeter with the sensitivity of 1,000 Ω/V, having scales of
0 - 100 V, 0 - 200 V and 0 - 300 V is used to measure the voltage between terminals a - b of a circuit.
The reading taken on the scale 0 - 100 V showed a value of 60 V and on the scale 0 - 300 V showed a value of 100 V as shown in Figure 16-06-1. Determine the true voltage between terminals a - b of the circuit.
Solution of the Problem 16-6
Note in Figure 16-06.1 that we represent the entire circuit as a voltage source E in series with a resistor R as we know from Thévenin's theorem. This way, based on the two tests, we can write a system of two equations with two unknowns. Then using the data provided in the problem statement
and through a voltage divider, for test 1 we can write:
Working algebraically the two equations above so that we have E in function of R and equating the two we obtain:
Solving this equality we easily determine the value of R, or:
Substituting this value, either in the equation for test 1 or test 2, we find the true value of the voltage between terminals a - b.
Keep in mind that the true value of Vab is when we have an open circuit at terminals a - b. Therefore, we easily conclude that:
