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Capacitance Bridge Working Principle

AC bridges are used for measurement of inductances and capacitances. All AC bridge circuits are based on Wheatstone bridge.

Figure 1(a) shows the circuit of a simple capacitance bridge. Cs is a precise standard capacitor, Cx is an unknown capacitance, and Q and P are standard resistors, one or both of which is adjustable. An AC supply is used, and the null detector (D) must be an AC instrument. A low-current rectifier ammeter is frequently employed as a null detector. Q is adjusted until the null detector indicates zero, and when this is obtained, the bridge is said to be balanced.

Fig.1: (a) Simple Capacitance Bridge

Working Principle of Capacitance Bridge

When the detector indicates null, the voltage drop across Cs must equal that across Cx, and similarly, the voltage across Q must be equal to the voltage across P. therefore,

$\begin{align}  & {{V}_{cs}}={{V}_{cx}} \\ & or \\ & \begin{matrix}   {{i}_{1}}{{X}_{cs}}={{i}_{2}}{{X}_{cs}} & \cdots  & (1)  \\\end{matrix} \\\end{align}$

And

\[\begin{align}  & {{V}_{Q}}={{V}_{P}} \\ & or \\ & \begin{matrix}   {{i}_{1}}Q={{i}_{2}}P & \cdots  & (2)  \\\end{matrix} \\\end{align}\]

Dividing equation (1) by equation (2):

\[\begin{matrix}   \frac{{{X}_{cs}}}{Q}=\frac{X{}_{cx}}{P} & \cdots  & (3)  \\\end{matrix}\]

Referring to equation (3) and figure 1(b), the general balance equation for all AC bridges can be written as:

Fig.1(b): General circuit diagram for an AC bridge

$\begin{matrix}   \frac{{{Z}_{1}}}{{{Z}_{2}}}=\frac{{{Z}_{3}}}{{{Z}_{4}}} & \cdots  & (4)  \\\end{matrix}$

Substituting 1/ωCs for Xcs , and 1/ωCx for Xcx in equation (3),

$\begin{align}  & \frac{1}{\omega {{C}_{s}}Q}=\frac{1}{\omega {{C}_{x}}P} \\ & or \\ & {{C}_{x}}=\frac{Q\omega {{C}_{s}}}{P\omega } \\\end{align}$

Giving

 

Formula for Unknown Capacitance
\[\begin{matrix}   {{C}_{x}}=\frac{Q{{C}_{s}}}{P} & \cdots  & (5)  \\\end{matrix}\]

It is seen that the unknown capacitance Cx can now be calculated from the known values of Q, Cs, and P.

About Ahmad Faizan

Mr. Ahmed Faizan Sheikh, M.Sc. (USA), Research Fellow (USA), a member of IEEE & CIGRE, is a Fulbright Alumnus and earned his Master’s Degree in Electrical and Power Engineering from Kansas State University, USA.

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