In a non-inverting op-amp configuration, the closed-loop gain is given by which expression?

• A. Gain = Rin/Rf.
• B. Gain = 1 + Rf/Rin.
• C. Gain = -Rf/Rin.
• D. Gain = Rin * Rf.

Answer: (B)

In a non-inverting amplifier, the feedback network sets the gain through a positive feedback path that ends at the inverting input, while the input signal goes to the non-inverting input. The resistor from output to the inverting node is Rf, and the resistor from that node to ground is Rin. The key idea is that, with an ideal op-amp, the inputs draw no current and V- (the inverting input) sits at the same voltage as V+ (the input voltage, Vin).

The voltage at the inverting node is a divider between the output and ground, so V- equals Vout times Rin divided by (Rin plus Rf). Since V- ≈ Vin, you can write Vin = Vout * Rin/(Rin + Rf). Rearranging gives Vout = Vin * (Rin + Rf)/Rin = Vin * (1 + Rf/Rin). So the closed-loop gain is 1 + (Rf/Rin), which is a positive, typically greater than 1, for this configuration.

Why the other expressions don’t fit: Rin/Rf would not produce the correct gain for a non-inverting setup and often implies a value less than or greater than 1 in a way that doesn’t match the actual divider behavior. The negative ratio -Rf/Rin is the gain of an inverting amplifier, where the input goes to the inverting terminal. The product Rin*Rf has units of ohm-squared and doesn’t represent a dimensionless gain.