In a noninverting amplifier, the closed-loop gain is

In a noninverting amplifier, the closed-loop gain is

• A. 1 + (Rf/Rin)
• B. Rf/Rin
• C. Rin/Rf
• D. 1

Answer: (A)

In a noninverting amplifier, the feedback network of Rf from output to the inverting input and Rin from the inverting input to ground sets the gain. The op-amp drives the output so that the inverting input voltage matches the noninverting input, so V- ≈ Vin. The current through Rin is Vin/Rin, and that same current flows through Rf, giving (Vout − Vin)/Rf = Vin/Rin. Solving for Vout yields Vout = Vin(1 + Rf/Rin), so the closed-loop gain is Vin-to-Vout equal to 1 + Rf/Rin. This matches the expression 1 + (Rf/Rin). The other forms would correspond to different configurations: Rf/Rin alone is the gain of an inverting amplifier, Rin/Rf is its reciprocal, and a gain of 1 would be just a unity-gain buffer with no amplification.

In a noninverting amplifier, the feedback network of Rf from output to the inverting input and Rin from the inverting input to ground sets the gain. The op-amp drives the output so that the inverting input voltage matches the noninverting input, so V- ≈ Vin. The current through Rin is Vin/Rin, and that same current flows through Rf, giving (Vout − Vin)/Rf = Vin/Rin. Solving for Vout yields Vout = Vin(1 + Rf/Rin), so the closed-loop gain is Vin-to-Vout equal to 1 + Rf/Rin. This matches the expression 1 + (Rf/Rin). The other forms would correspond to different configurations: Rf/Rin alone is the gain of an inverting amplifier, Rin/Rf is its reciprocal, and a gain of 1 would be just a unity-gain buffer with no amplification.