Problem 54-1    Source:  Problem 6.26 - page 103 - EDMINISTER, Joseph A. - Book: Circuitos Elétricos - Ed. McGraw Hill - 1971

The voltage drop at the j2 reactance of the series circuit in the Figure 54-1.1 is V_L = 13.04 ∠+15°. Determine the value of Z.

Solution of the Problem 54-1   

You can calculate the electric current I, which circulates through the series circuit, as the problem provides the value of V_L. Using Ohm's law and remembering that j2 = 2 ∠90°, we get:

It is possible to calculate the equivalent impedance that the series circuit presents to the voltage source. Again, using Ohm's law, we have:

Performing the calculation we find for the value of Z_eq:

But Z_eq represents the total impedance of the series circuit. Therefore, the sum of all components that make up the circuit must be equal. So, we can write:

Carrying out the calculation, the value of Z is:

Thus, for the equivalent impedance to have this value, the values of R and X_C that form the impedance Z, must be: