**Objective:-**

To measure the unknown loss free capacitance by balancing the De-Sauty’s bridge.

**Theory:**

De-sauty’s bridge provides us the most suitable method for comparing the two values of capacitor if we neglect dielectric losses in the bridge circuit.

This bridge measured an unknown capacitance in terms of a standard capacitance of capacitor i.e. Comparing two capacitances to ratio arms of this bridge. In which, one arm of the bridge consists of pure resistance and other arm two capacitors (where one is known capacitance and another is standard capacitance).

let

C_{1}=cap whose capacitance to be measured.

C_{2}=a standard capacitor.

R_{3}, R_{4}=non-inductive resistors.

the circuit of de sauty’s bridge is shown in figure in the circuit diagram, battery is applied between terminals marked as 1 and 4. The arm 1-2 consists of capacitor C_{1}(whose value is un known) which carries current i_{1}as shown, arm 2-4 consist of pure resistor (here pure resistor means we assume it non-inductive in nature), arm 3-4 also consists of pure resistor and arm 4-1 consist of standard capacitor whose value is already known to us.

Balance is obtained by varying either R_{3} or R_{4} for balance, point 1 and 2 are at same potential.

I_{1}R_{4}=I_{2}R_{3}

Or, (-j/ѠC_{1}) ×R4=(-j/ѠC_{2}) ×R_{3}

Dividing one equation by another,

C_{1}/C_{2}=R_{4}/R_{3}

Or, C_{1}=C_{2}×(R_{4}/R_{3})

The bridge has maximum sensitivity when C_{1}=C_{2}.

Therefore, Balance condition: C_{1}=C_{2}×(R_{4}/R_{3}).

Where, C_{1} is the unknown capacitor.

In order to obtain the balance, point we must adjust the values of either R_{3} or R_{4 }without disturbing any other element of the bridge. This is the most efficient method of comparing the two values of capacitor if all the dielectric losses neglected from the circuit.

**Phasor diagram:**

The phasor diagram of de sandy bridge is shown in figure

Let,

The voltage drops across unknown capacitor be E_{1}

Voltage drop across the resistance R_{3} be E_{3}

Voltage drop across arm 3-4 be E_{4}

Voltage drop across arm 4-1 be E_{2}

At the balance condition the current flows through 2-4 path will be zero and also voltage drops E_{1} and E_{3} be equal to voltage drops E_{2} and E_{4} respectively.

In order to draw the phasor diagram E_{3}(or E_{4}) are taken as reference axis, E_{1} and E_{2 }are shown at right angle to E_{1}(or E_{2}). As capacitor is connected therefore phase difference angle obtained is 90°

**Apparatus Used:**

**Procedure:**

- Measure the amplitude and frequency of the dredge oscillator by the help of CRO.
- Obtain square wave output, of amplitude of 9v and frequency of 1khz from the bridge oscillator.
- Connect the de-sauty bridge kit by the help of path cords and other apparatus as descripted in circuit diagram.
- Connect head phone detector to the circuit of detection of the balanced condition of the bridge.
- Vary the resistance R
_{3}and R_{4}and capacitor C_{2}and observe the output sound from the headphone detector. - If the output sound from the head phone detector is very low, then that very condition is considered to be balanced condition of the bridge. Else the bridge is considered to be at unstable condition.
- Note down three points of unstable condition by varying the R
_{3}and R_{4}and capacitor C_{2}. - Tabulate the readings based on the value of unknown capacitance by the equation C
_{1}=C_{2}×R_{4}/R_{3}

**Calculations:**

**Conclusion:**