Solving AC circuits by loop current methods

Solving AC circuits by loop current methods

[Very Important Note: The student should be thorough with the conversion of rectangular to polar and vice versa before he solves the problems on A.C. He can refer the introduction pages for help]

Example 6 Apply mesh current method and determine currents through the resistors of the network shown in fig.1.79.

Solution: By inspection,

[Hint: The student is advised to solve the problem by simplification of series parallel combination of impedances.]

Example 7 In the network shown in figure find V2 such that the current in the (1+j1) Ω branch is zero.

Solution: The directions of the loop currents are already given in the problem. Without changing the directions, the problem is solved.

Given that, the current through (1+j1) Ω = 0

i.e., I2 = ∆2/ ∆ =0

Hence, ∆2 = 0

= 96 < 37° volts In the matrix form, we get the loop 

equation as below

Example 8 In the network shown in figure determine V2 such that the current in the 2+ j3 impedance is zero.

Solution: The directions of the loop currents here are not given. Hence, let us assume that they are all clockwise. Since the current through (2 + j3) is given to be zero, I2 = 0 => ∆2/ ∆=0 Hence the condition

 Δ2=0, So, by inspection

Example 9 In the network shown in the figure the source V1 results in a voltage V0 across the (2-j2)Ω impedance. Find the source V1 which corresponds to V0=5<0° volts.

Solution: Let the loop currents be I1, 12 and I3.