What is the closed-loop gain formula for an inverting amplifier, and what is the role of the virtual ground?

What is the closed-loop gain formula for an inverting amplifier, and what is the role of the virtual ground?

• A. Gain = 1 + (Rf/Rin); virtual short between inputs
• B. Gain = -Rf/Rin; the inverting input sits at virtual ground (approximately 0 V) due to negative feedback, causing current through Rin to flow through Rf.
• C. Gain = -Rin/Rf; current flows through Rin in reverse direction
• D. Gain = Rin/Rf; incorrect sign

Answer: (B)

The key idea is that negative feedback in an inverting amplifier forces the inverting input to sit at a virtual ground. Since the non-inverting input is connected to real ground, the op-amp adjusts its output so the inverting input is driven to about 0 V, even though it isn’t physically connected to ground. With this virtual ground, the input current through Rin is Vin/Rin, and because the op-amp input current is essentially zero, that same current must flow through the feedback resistor Rf. The drop across Rf is then -Vout, so Vin/Rin ≈ -Vout/Rf. Rearranging gives Vout = - (Rf/Rin) Vin. The negative sign shows that the output is inverted relative to the input, and the magnitude is set by the ratio Rf/Rin. This description matches the closed-loop gain formula for an inverting amplifier: Vout/Vin = -Rf/Rin, with the inverting input held at a virtual ground (approximately 0 V) by negative feedback. The other forms either describe a different topology (non-inverting gain) or use the wrong ratio or sign, so they don’t apply to this configuration.

The key idea is that negative feedback in an inverting amplifier forces the inverting input to sit at a virtual ground. Since the non-inverting input is connected to real ground, the op-amp adjusts its output so the inverting input is driven to about 0 V, even though it isn’t physically connected to ground. With this virtual ground, the input current through Rin is Vin/Rin, and because the op-amp input current is essentially zero, that same current must flow through the feedback resistor Rf. The drop across Rf is then -Vout, so Vin/Rin ≈ -Vout/Rf. Rearranging gives Vout = - (Rf/Rin) Vin. The negative sign shows that the output is inverted relative to the input, and the magnitude is set by the ratio Rf/Rin.

This description matches the closed-loop gain formula for an inverting amplifier: Vout/Vin = -Rf/Rin, with the inverting input held at a virtual ground (approximately 0 V) by negative feedback. The other forms either describe a different topology (non-inverting gain) or use the wrong ratio or sign, so they don’t apply to this configuration.