Problem 7.3   Source:   Problem elaborated by the author of the site.

For the circuit shown in the Figure 07-03.1, the potentiometer P1 varies its resistance from 0 to 50Ω. Make a graph showing the eletric power dissipated in the resistor R1 when we vary the potentiometer throughout its range.

Solution of the Problem 7.3

In the Figure 07-03.2, we notice that the part of the circuit highlighted in green can be disregarded since is in parallel with the voltage source of 35 volts. Likewise, the part that is highlighted in blue can also be eliminated because it is in parallel with the voltage source of 15 volts.

With this simplification, the circuit is reduced to that shown in the Figure 07-03.3. It is clear that the sources of are in series, so we can add them and work with a single source of 50 volts.

Since we want to calculate the power dissipated in R₁, we can assume that it is a load for the voltage source in series with the potentiometer. As the statement of the problem asks to draw a graph of power in R₁, then we will calculate several power values. Therefore, we must give different values to P₁.

With each value of P₁ we calculate the electric current I, indicated by the blue arrow in the circuit and thus we will have to calculate the power dissipated in R₁. Initially we will do P₁ = 0 . Then the current will be the voltage of 50 volts divided by R₁, or:

With value of the I we can calculate the power dissipated in R₁, or:

Doing similarly for other values of P₁, we can assemble the Table 07-01.