The inverting amplifier uses negative feedback to control the gain. R_f provides the feedback.

Gain = V_out / V_in

Gain = - R_f / R₁

V_out / V_in = - R_f / R₁

 

R_f and R₁ control the GAIN. The formula has a minus sign in it because the amplifier inverts the input signal.

The input resistance (impedance) of this circuit is equal to R₁.

The inverting input, labelled "P", is a Virtual Earth because the voltage here is approximately zero as long as the amplifier is not limiting. If the real-life op' amp' had a gain of 1000000, only -10µV would be needed at point P to give +10V output. This tiny voltage is so small, it is assumed to be zero for all normal circuit calculations.