Problem 15-12    Source:    Problem elaborated by the author of the site.

Determine the value of R, in the circuit shown in Figure 15-12.1, knowing that the voltage source of 100 volts provides the circuit with a power of 500 watts.

Solution of Problem 15-12

Note that the resistor of 9 ohms in series with the current source 2 V_a can be eliminated without prejudice to the solution of the problem. So in the Figure 15-12.2 we can see the circuit already simplified.

Note that in this circuit the current I, which leaves the source of 100 V, can be calculated easily with the data provided by the problem as we know that the voltage source provides the circuit a power of 500 watts. So:

Let's find the value of I_a by doing the equation for node 1 , that is:

From this we easily conclude that:

So we can calculate the value of V_a, or:

Knowing the values of I and V_a we can calculate the values of V₁ and V₂, or:

Knowing the value of V₂ we can make the mesh passing through the controlled source 10 I_b and calculate the value of I_b, so:

Since we know the value of I_a , so we have an equation and an unknown. Doing the numerical substitution and making the calculation, we find:

With the value of I_b we easily calculate the value of V₃, or:

This is the voltage that is over R. To determine its value it is necessary to know the current that goes through her. Making the equation of node 3 easily calculate this current, remembering that the source 2 V_a = 2 x 10 = 20  A.

By substituting the variables for their numeric values and performing the calculation, we find:

We are now able to calculate the value of R, or: