Question

A sensor is incorporated in a capacitance measuring circuit as shown in the following figure. Assuming ideal op amp, the output voltage under the conditions mentioned $\left(C_1\text{and}{C}_2\text{are 14.17 pF and 21.25 pF respectively}\right)$ is

• A. 0.012V
• B. 0.354 V
• C. 1.23 V
• D. 2.541 V

Answer 1

The correct option is B 0.354 V


$V_{+}=0V$

$\text{Using virtual ground,}$

$V_{+}=V_{-}=V_A=0V$

$\text{Apply KCL at node A,}$

$I_1+I_2+I_3=0$

$\frac{V_A-V_p}{1/j\omega C_1}+\frac{V_A+V_p}{1/j\omega C_2}+\frac{V_A-e_0}{1/j\omega C_3}=0$

$Put{V}_A=0V,$

$V_p=1V$

$e_0=\left[\frac{C_2-C_1}{C_3}\right]1V$

$=\left[\frac{21.25\times {10}^{-12}-14.17\times {10}^{-12}}{20\times {10}^{-12}}\right]\times 1$

$=0.354V$