Theory

Let,

C₁=capacitor whose capacitance is to be measured.

r₁= a series resistance representing the loss in the capacitor C₁.

C₂= a standard capacitor.

R₃= a non inductive resistance.

C₄= a variable capacitor.

R₄= a variable non inductive resistance.

At balance,

$$ (r_1+\frac{1}{j \omega C_1}) * (\frac{R_4}{ j \omega C_4R_4+1}) = \frac{R_3}{j \omega C_2}......(1) $$

$$ r_1R_4-\frac{jR_4}{\omega C_1} = - \frac{jR_3}{\omega C_2} + \frac{R_3R_4C_4}{C_2}......(2) $$

Or Equating the real and imaginary terms in equa. (2), we obtain

$$ r_1 = R_3*\frac{C_4}{C_2}......(3) $$

$$ C_1 = R_4* \frac{C_2}{R_3}......(4) $$

And, Two independent balance equations (3) and (4) are obatined if C₄ and R₄ are chosen as the variable elements.

Dissipation factor

$$ D_1 = \omega C_1r_1......(5) $$