HW4

1. Gain of the non-inverting amp

   \;=\; 1 + \frac{9\,\mathrm{k}\Omega}{1\,\mathrm{k}\Omega} \;=\; 10.$$

2. Nodal analysis at the $+$ input ($V_{+}$)
   The three resistors connect $V_{+}$ to:

   • a $+2$V source through $20$kΩ
   • a $-5$V source through $40$kΩ
   • ground through $40$kΩ

   Write KCL:

   $$\frac{V_{+}-2}{20\mathrm{k}\Omega }+\frac{V_{+}-(-5)}{40\mathrm{k}\Omega }+\frac{V_{+}-0}{40\mathrm{k}\Omega }=0$$

   Multiply by $40\mathrm{k}\Omega$:

   $$2(V_{+}-2)+(V_{+}+5)+V_{+}=0⟹4V_{+}+1=0⟹V_{+}=-0.25\text{ V}.$$

3. Output voltage
   $V_{\mathrm{out}}=\text{Gain}\times V_{+}=10\times (-0.25)=-2.5\text{ V}.$