Question

HI,

Can someone help with this question with steps:)? Thanks in advance:)

(Kirchoff's Laws) Kirchoff's voltage and current laws apply for general impedances just like they do for resistor networks. For the circuit given here, find Ii(w), I2() and I3 (w). The answer should look like li (w)-Fi (R. L . C. a) x y (for J-11. 2.3]), where the Fi (R. L. C. w) are some complicated formulae. Since these formulae get complicated. I do not expect the simplest closed form for the answer. I do expect that you solve the system of equations (it should be reducible to a system of two equations in two unknowns) and present the answers in the above form with a single V and I, (j-1,2, 3) and no other voltages or currents in the answer. 12 3

Answer 1

In loop 1 by kirchoff voltage law -v + I_1/j w c + I_3 R = 0 V = I_1/j w c + I_3 R in loop 2 (I_1 - I-3) j w L - I_3 R = 0 I_1 kj w L = I_3 R + I_3 j w L I_1 = I_3 (R + j w L)/j w L putting I_1 into 1 we get V = I_3/j w c(R/j w L = 1) + I_3 R V = I_3(-R/w^2 L c + 1/j w c) + I_3 R I_3 = V/R - R/W_KL L C + 1/j w c putting this I_3 into 2 we get \r\n I_1 = (R/j w L + 1) (v/(R + 1/j w c - R/w L L c)) and I_2 = I_1 - I_3 I_2 = V/(R + 1/j w c - R/W L L c) (r/j w L) + V/R + 1/ j w c - R/w L L c -v/r - r/w^2 L C = 1/j w c I_2 = V/(R + 1/j w c - R/w^2 L c) (r/j w L)