Problem 55-9    Source:   Problem 2 - List of RLC Problems - Discipline Electrical Circuits of the School of Engineering - UFRGS - 2017 - Prof. Dr. Valner Brusamarello.

In the circuit shown in the Figure 55-9.1, determine V_ab.

Solution of the Problem 55-9   

Notice that the capacitor -j4, being in parallel with the voltage source can be eliminated from the circuit without prejudice to the solution. In addition, the capacitor -j5 is in series with the inductor j5 canceling each other out. So we are left alone with the resistor of value 1 ohm in series with the voltage source. On the other hand, on the right side of the circuit, there is a capacitor, -j2, in series with the inductor j2 that are also canceled. This way we have a short circuit between the points 1 and 2. This causes that there is no current flow through the two resistors of value R. Therefore, it is enough to calculate the voltage drop in the inductor, since this will be equal to V_ab. To do so, we must calculate the current I that flows through the inductor. Since there is only the 1 ohm resistor in the circuit, we have:

Therefore, the voltage V_ab is given by: