Circuit Theory/Phasors/Examples/example11/phasor solution/code2
This problem was done three different ways, because simulation at circuitlab.com doesn't match.
Kirchhoff
editnumeric::linsolve([v1 = i1, v2=2*i2, ic = 2*I*vc, vL = I*iL, i1-i2-ic-sqrt(3)-I=0, ic-iL + sqrt(3)+I =0, v1 + v2 -5 =0, vc + vL - v2 =0],[i1,i2,ic,iL,v1,v2,vc,vL])
Some Substitution
editnumeric::linsolve([i1-i2-sqrt(3)-I - ic, ic - iL + sqrt(3) + I, i1 + 2*i2 - 5, ic/(2*I) +I*iL-2*i2],[i1,i2,ic,iL])
Node
editnumeric::linsolve([5-v2 - sqrt(3) -I - v2/2- 2*I*(v2-vL), 2*I*(v2-vL) + sqrt(3) + I - vL/I],[v2,vL])
The node method hasn't been covered yet. But look at the analysis. It finds two voltages rather than every thing. It finds voltages instead of currents as "junction equations" do in Kirchhoff.