Determine the output voltage for the circuit, if $V_2 = 5v$ and $V_2 = 3v$

Solution: Consider only $V_1$ is applied and $V_2$ is $V_1$ is grounded.

To find $v_x$

$= \frac{20k}{20k + 20 k} \times 5v$

$\frac{20k}{40k} \times 5v$

= 2.5v

$V_0^1 (1+ \frac{100k}{100k} ) v_2$

$V_0^1 = 2 \times 2.5v$

$V_0^1 = 5v$ ------- (1)

Consider only $V_2$ is applied and $V_1$ is grounded.

$V_0^11 = \frac{-100k}{100k} \times v_2$

$= -v_2$

$V_0^11 = -3V$

$\therefore$ $v_0 = v_0^1 + v_0^11$

= 5 - 3

$V_0 = 2V$