Problem with connecting two voltage sources in series

[want_to_know]

Hi,

Please forgive me for a simple question like this, I am new to this area, and was trying to understand how two voltage sources work when connecting in series.

Please refer to figure 1, I set R=0.0001 ohm, L =0.01 H,

Vb = 10.001V, frequency = 1, phase shift = 0
Vg = 10V, frequency = 1, phase shift = 0

Having the above parameters, i obtained results as in Figure 3 (current measurement), it can be seen that the current value is around 0.03A, from manual calculation, I got 0.016A, I wonder what is wrong with my calculation?

For another test, all parameters are the same except that I change the phase shift of Vg to pi/2. Referring to Figure 2 (again it is current measurement), it can be seen that the current value is now around 380A.

I have no idea how to calculate the current value in both cases, appreciate any guidance or links for me to understand this very basic problem.

Apologize for such a simple question.

Thanks.

 

[D.A.(Tony)Stewart]

Sum of all the voltages in a Loop = 0V (Kirchoff Law) is the mathematical approach, so one here is positive and the other looks negative in a loop as both (-) side are together.

Intuitive approach is the RL load sees the difference voltage between V1 and V2 which have a common ground and both ideal 0 ohm source impedance.

As defined the difference is 0.001Vac at f=1

This is a simple model of circulating current when sources are mismatched and no load in the middle to ground.
Imagine two power stations on the grid matched to 1 part in 10 thousand (except this is low voltage zero ohms)

 

[want_to_know]

Sum of all the voltages in a Loop = 0V (Kirchoff Law) is the mathematical approach, so one here is positive and the other looks negative in a loop as both (-) side are together.

Intuitive approach is the RL load sees the difference voltage between V1 and V2 which have a common ground and both ideal 0 ohm source impedance.

As defined the difference is 0.001Vac at f=1

hi, thanks for your reply, I understand that by applying Kirchoff Law,
IZ+Vg-Vb=0
I = (Vb-Vg)/(Z)

For the case where both phase shift are zero, I calculated I value from the above equation, Z=0.0628

I= 0.001/0.0628 = 0.016 A

but the simulation result gives 0.03A, what did I miss? Please let me know, I think this should be very simple, shame on me