Question

A differential push-pull type capacitive displacement sensor (nominal capacitance $C_0=0.01\mu F)$ is connected in two adjacent arms of an ac bridge in such a way that the output voltage of the bridge is independent of the frequency of the supply voltage. Supply to the bridge is 1 V at 1 kHz and two equal resistances $(R=3.9K\Omega )$ are placed in the other two arms of the bridge. The bridge sensitivity is

• A. 0.001 mV/pF
• B. 0.05 mV/pF
• C. 0.1 mV/pF
• D. 0.5 mV/pF

Answer 1

The correct option is B 0.05 mV/pF


$\text{Taking}\Delta C\text{of the order of pF}\left({10}^{-12}F\right)$

$V_a=\frac{R}{R+R}\times 1=\frac{1}{2}=0.5V$

$V_b=\frac{0.001+\Delta C\times {10}^{-}6}{0.01+\Delta C\times {10}^6+0.01-\Delta C\times {10}^6}\times 1$

$=\frac{0.01+\Delta C\times {10}^{-6}}{0.02}$

$V_0=V_b-V_a$

$V_0=\frac{0.01+\Delta C\times {10}^{-6}-0.5\times 0.02}{0.02}$

$V_0=\frac{\Delta C\times {10}^{-6}}{0.02}=50\times {10}^{-6}\Delta C$

$\therefore \frac{V_0}{\Delta C}=50\times {10}^{-6}V/pF=0.05mV/pF$