DC and AC voltage with Kirchoff's rule?

Question

Would this equation work well for DC voltage: (Vab^2 Vbc^2)^1/2? Explain. Why doesn't Kirchhoff's rule: Vab Vbc = Vac work well for an AC source? How would Kirchoff's rule (stated above) work with a DC source?

Thank you for your help!

Answer 1

Kirchhoff's rules for current and voltage are applicable for both  DC and AC. However for AC and the presence of reactive components such as inductors L and capacitors C requires one   to use phaser mathematics for the computations.

For example  |Vac|= sqrt  (Vab^2 + Vbc^2) or as you have stated |Vac|= (Vab^2 + Vbc^2)^1/2  is applicable to AC circuit with C and/or  L present.  

Phasers are electric vectors, therefore

Vac = Vab + Vbc  is still fine however one has to keep in mind that it is a vector addition, or addition of vectors in two dimensions.

Finally

|Vac|= sqrt  (Vab^2 + Vbc^2)  

with an angle

arctan ( Vac (imaginary) / Vac (real))

Does that answer your question.