Problem 16-4    Source:    Problem elaborated by the author of the site.

A voltmeter with the sensitivity of 2 000 Ω/V, having scales of  0 - 100V and 0 - 300V,  is used to measure the voltage between the terminals a - b of a circuit. When the 0 - 100V scale was used, the voltmeter showed a reading of 80 volts. When the scale used was 0 - 300V, the reading of the voltmeter was 120 volts. Calculate the true voltage between the terminals a - b .

Solution of the Problem 16-4

Initially, the value of the internal resistance of the voltmeter in the two scales is calculated. For the scale of 100 volts, we have:

Now for the scale of 300 volts, we have:

In the Figure 16-04.1 shows the equivalent circuit we will use to solve the problem. The voltage V_th represents the actual voltage that should be measured by an ideal instrument. The resistance R_th, represents the equivalent resistance that the circuit offers, via terminals a - b, to the multimeter. V_volti represents the voltage read by the multimeter.

And finally, R_i is the internal resistance of the multimeter in the selected range. Note that, knowing the value of V_volti and R_i, in the analyzed scale, it is possible to calculate the value of i. Taking this procedure to the two readings, we obtain a system of two equations with two unknowns of easy solution.

Thus, by calculating the value of i for the scale of 100 volts.

For the scale of 300 volts:

Based on the circuit shown in the figure above and making the mesh equations of voltage for these two situations, we find the system of equations.

Then, replacing the numerical values for each situation:

Just equate the two equations, we find:

Therefore, the true voltage is 160 volts and the equivalent resistance of the circuit under measurement, between the points a - b is 200 000 Ω.