What is the closed-loop gain in this op amp circuit?
Assuming this is a problem from a book and we can assume ideal parameters to the opamp where no specifications are otherwise given, then:







simulate this circuit &ndash; Schematic created using CircuitLab

Assuming the equivalent circuit at the top for the opamp, the nodal equations are:

$$\begin{align*}
\frac{V_X}{R_1}+\frac{V_X}{R_2}+\frac{V_X}{R_{IN}}&amp;=\frac{V_O}{R_1}+\frac{V_S}{R_{IN}}\\\\
\frac{V_O}{R_1}+\frac{V_O}{R_3}+\frac{V_O}{R_{OUT}}&amp;=\frac{V_X}{R_1}+\frac{\left(V_S-V_X\right)\cdot A_\text{OL}}{R_{OUT}}\\\\\therefore\\\\V_X&amp;\approx 0.999955\cdot V_S\\\\V_O&amp;\approx 8.999593\cdot V_S
\end{align*}$$

The script I used in sympy (worth getting) is:

var('r1 r2 r3 ri ro aol vo vx vs')
e1=Eq(vx/r1+vx/r2+vx/ri,vo/r1+vs/ri)
e2=Eq(vo/r1+vo/r3+vo/ro,vx/r1+(vs-vx)*aol/ro)
ea=solve([e1,e2],[vx,vo])
    { vo: r1*r3*vs*(aol*(r1*r2 + r1*ri + r2*ri) - r2*(aol*r1 - ro))/(r2*r3*ri*(aol*r1 - ro) + (r1*r2 + r1*ri + r2*ri)*(r1*r3 + r1*ro + r3*ro)),
      vx: r1*r2*vs*(aol*r3*ri + r1*r3 + r1*ro + r3*ro)/(r2*r3*ri*(aol*r1 - ro) + (r1*r2 + r1*ri + r2*ri)*(r1*r3 + r1*ro + r3*ro))
    }
ea[vx].subs({aol:2e5,ri:2e6,ro:50,r1:40e3,r2:5e3,r3:20e3})
0.999954839544092*vs
ea[vo].subs({aol:2e5,ri:2e6,ro:50,r1:40e3,r2:5e3,r3:20e3})
8.99959265268771*vs


Just nodal is enough here. The main thing is to figure out the opamp model from the specs you were given.