Problem 55-8   Source:   Problem 9.29 - page 263 -    NILSSON & RIEDEL -    Book: Circuitos Elétricos - 8ª edição - Ed. Pearson - 2010.

In the Figure 55-8.1, we know that    R = 25 Ω ,   R₁ = 160 Ω ,   R₂ = 120 Ω ,   jX_L = j40 Ω    and    -jX_C = -j80 Ω. The value of the source is   I_N = 40 + j80 mA.  On the other hand, we know that   i_L= 40∠0° mA.

a) Determine i_C , i and V.

b) Make a phasor diagram of the currents and voltages of the circuit.

Solution of the Problem 55-8   

Calling of Z_L the impedance through which it circulates i_L and of Z_C the impedance through which it circulates i_C, we can write:

As we know the value of i_L, so to calculate V_N just use the Ohm's law, or:

Performing the multiplication:

Note that the current value is at mA and has become V_N to volts. In possession of the value of V_N, we can calculate the value of i_C. Simply divide the value of V_N by the impedance Z_C:

Applying the law of nodes to the circuit, we can calculate the value of i, since it is the phasor sum of the other three currents, that is:

By making the numerical substitution of the values:

And so, the value of i is:

See the diagram in the Figure 55-8.2 for the phasors of all the currents involved in the circuit. Notice that i_C is in phase with i, both advanced 45° about i_L.

As we know the value of V_N and i, we can calculate the value of V. For this, it is enough to make the mesh between V, R and V_N, that is:

Making the numerical substitution and performing the calculation:

And finally, in the Figure 55-8.3, the phasors of all the voltages involved in the circuit. Notice that V_Ri is in phase with i, and advanced by 45° with respect to i_L.