Question

The level of a liquid is to be measured using concentric cylinder capacitive arrangement, following specification defines the system:

Permittivity of liquid = 25

Cylinder separation = 5 mm

Plate area = $\eta$. R. L

R = Radius = 6 cm

L = Distance along the cylinder.

The range of capacitance variation as the liquid level varies from 0 to 10 m in a 10 m tank is ?

• A. $6.672nF-167nF$
• B. $6.672\mu F-167\mu F$
• C. $6.672pF-167pF$
• D. None of these

Answer 1

The correct option is A $6.672nF-167nF$

$\text{The capacitance is given by,}$

$C=\frac{{ϵ}_o{ϵ}_{r}A}{d}$

$\text{Given ,}{ϵ}_r\text{for liquid = 25}$

$\text{Capacity of entire cylinder:}$

$A=2\pi RL=2\pi \times 6\times {10}^{-2}\times 10$

$=3.7699m^2\approx 3.77m^2$


$\text{Capacitance without liquid,}$

$C_1=\frac{{ϵ}_r{ϵ}_{o}A}{d},{ϵ}_r=1\left(Air\right)$

$C_1=\frac{8.85\times {10}^{-12}\times 3.77}{0.005};{ϵ}_o=\text{free space permitivity}$

$=6672.9\times {10}^{-12}F$

$=6.672nF$

$\text{Now capacitance with liquid}$

$C_2={ϵ}_r{C}_1$

$=25\times C_1$

$=25\times 6.672nF=166.8nF$

$=167nF$