What is the closed-loop gain Av of an inverting amplifier with feedback resistor Rf and input resistor Rin, using an ideal op-amp?

What is the closed-loop gain Av of an inverting amplifier with feedback resistor Rf and input resistor Rin, using an ideal op-amp?

• A. Av = Rin / Rf
• B. Av = -Rin / Rf
• C. Av = -Rf / Rin
• D. Av = Rf / Rin

Answer: (C)

In an ideal op-amp configured as an inverting amplifier, the inverting input sits at a virtual ground because the amplifier adjusts its output to keep both inputs at the same voltage under negative feedback. The input signal Vin passes through Rin to that node, and feedback from the output through Rf also connects to the same node. With the inverting input held near 0 V, the current through Rin is Vin/Rin, and this same current must flow through Rf toward the output. The output voltage is then Vout = - (Vin / Rin) * Rf, giving a closed-loop gain of Av = Vout / Vin = -Rf / Rin. The negative sign indicates inversion, and the magnitude is set by the ratio Rf/Rin.

In an ideal op-amp configured as an inverting amplifier, the inverting input sits at a virtual ground because the amplifier adjusts its output to keep both inputs at the same voltage under negative feedback. The input signal Vin passes through Rin to that node, and feedback from the output through Rf also connects to the same node. With the inverting input held near 0 V, the current through Rin is Vin/Rin, and this same current must flow through Rf toward the output. The output voltage is then Vout = - (Vin / Rin) * Rf, giving a closed-loop gain of Av = Vout / Vin = -Rf / Rin. The negative sign indicates inversion, and the magnitude is set by the ratio Rf/Rin.