Write \$V_{A}\$ in terms of \$V_{in}\$ and the resistor values algebraically in a Op-Amp

Question

Consider the Op-Amp circuit in Fig. Q1(a). Write \$V_{A}\$ in terms of \$V_{in}\$ and the resistor values algebraically.

My Try

• Case 1 :

  I see wire(+) as opened since it draw almost 0 current ideally. So, we have

$$V_A=V_{in}\left(\frac{R_3}{R_3+R_4}\right)$$

• Case 2 :

  Transform the circuit as if the following one. Since wire(+) and wire(-) ideally have no potential difference, I shorted them together.

^{simulate this circuit – Schematic created using CircuitLab}

$$
R_{13}=\left(\frac{1}{R1}+\frac{1}{R3}\right)^{-1}\space \space \space \space and\space \space \space \space R_{24}=\left(\frac{1}{R2}+\frac{1}{R4}\right)^{-1}
$$

$$
R_{eq}=R_{13}+R_{24}
$$

Therefore,
$$
V_A=V_{in}\left(\frac{R_{13}}{R_{eq}}\right)
$$

My Questions

1. For Case 1 and Case 2, which one is correct? Or, both are wrong?
2. How to find the current I from \$V_{A}\$ to \$V_{out}\$? Can I calculate it from the following equation?

$$
I=\frac{0-V_A}{R_1}+\frac{V_{in}-V_A}{R_2}
$$

Thank you for your help.