If Rin is halved while Rf remains fixed, the closed-loop gain magnitude doubles.

If Rin is halved while Rf remains fixed, the closed-loop gain magnitude doubles.

• A. It remains unchanged
• B. It quadruples
• C. It doubles
• D. It halves

Answer: (C)

In an inverting op-amp, the closed-loop gain magnitude is set by the ratio Rf/Rin. With an ideal op-amp, Vout = - (Rf/Rin) Vin, so the magnitude is |Vout/Vin| = Rf/Rin. If Rin is halved while Rf stays fixed, the ratio becomes Rf/(Rin/2) = 2(Rf/Rin). Therefore the output amplitude doubles (the sign remains negative, so the output inverts). This is why the gain magnitude doubles when Rin is halved.

In an inverting op-amp, the closed-loop gain magnitude is set by the ratio Rf/Rin. With an ideal op-amp, Vout = - (Rf/Rin) Vin, so the magnitude is |Vout/Vin| = Rf/Rin. If Rin is halved while Rf stays fixed, the ratio becomes Rf/(Rin/2) = 2(Rf/Rin). Therefore the output amplitude doubles (the sign remains negative, so the output inverts). This is why the gain magnitude doubles when Rin is halved.