Question

Determine the gain of the op-amp circuit in Fig. E4.2.

Answer 1

\( Solution: \)

\( Step1 \)

The circuit is redrawn as shown in Figure 1

\( Step2 \)

write the node equation at the inverting terminal

\( I_1=I_2 \) => \( \frac{V_ --0}{R_1}=\frac{V_0-V_-}{R_2} \)

Apply ideal op-amp conditions\( \). \( V_-=V_+ \) and \( i_-=i_+ \)

Substitute the values \( V_S \) for \( v_- \) in the expression

\( \frac{V_ --0}{R_1}=\frac{V_0-V_-}{R_2} \)

\( \frac{V_s}{R_1}=\frac{V_0-V_s}{R_2} \)

\( \frac{V_0}{R_2}=V_s \bigg(\frac{1}{R_1}+\frac{1}{R_2} \bigg) \)

\( \frac{V_0}{V_s}=1+\frac{R_2}{R_1} \)

Answer 

Therefore, the gain of the op-amp is \( 1+\frac{R_2}{R_1} \)