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I simulated the following circuit:

enter image description here

Why is Vu=7.5 V? I expect there to be an error because Vu=5=10 at the same time.

The current in the two branches is the same, thus (R1=R2):

$$Vu=R_1 i+V_1$$

$$Vu=R_1 i+V_2$$

$$V_1=5=V_2=10$$

Thank you in advance.

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  • \$\begingroup\$ Do you know KCL ? \$\endgroup\$ – Long Pham Jul 20 '18 at 9:08
  • \$\begingroup\$ Hello @LongPham see edit please. \$\endgroup\$ – Gennaro Arguzzi Jul 20 '18 at 9:25
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Your equations are incorrect. If you define the current in one way, then that current needs to be negative for the other side.

$$\begin{align} V_u &= R\cdot i + V_1 \\ V_u &= -R\cdot i + V_2 \\ \end{align}$$

$$\begin{align} R\cdot i &= V_u - V_1 \\ R\cdot i &= V_2 - V_u \end{align}$$

You find that

$$V_u = \frac{V_1 + V_2}{2}$$

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