OPAMP Closed Loop Non Inverting Amplifier Formula Derivation

Before starting this take a look at this tutorial on, closed loop inverting amplifier.

Formula Derivation:

$ I_i = \frac{0 - v_i}{R_i} $

$ I_f = \frac{v_i - v_o}{R_f} $

since, there is no current flow between positive and negative pins,

$ I_i = I_f $

Now,

\begin{align} \frac{0 - v_i}{R_i} & = \frac{v_i - v_o}{R_f} \\ \frac{- v_i}{R_i} & = \frac{v_i - v_o}{R_f} \\ - v_i & = \frac{R_i}{R_f}(v_i - v_o) \\ \frac{R_f}{R_i} & = \frac{(v_i - v_o)}{- v_i} \\ \frac{R_f}{R_i} & = - 1 + \frac{v_o}{v_i} \\ \frac{v_o}{v_i} & = \frac{R_f}{R_i} + 1 \\ v_o & = v_i ( 1 + \frac{R_f}{R_i} ) \end{align}

The output voltage formula,

$ v_o = v_i ( 1 + \frac{R_f}{R_i} ) $