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Measurement of Unknown frequency using Wein’s bridge.

 

 

Object: Measurement of Unknown frequency using Wein’s bridge.

Apparatus Required

  Wein’s bridge, connecting wires, Head phone.

Theory

 Wien Bridge shown in Fig. 2.1 has a series RC combination in one and a parallel combination in the adjoining arm. Wien's bridge in its basic form is designed to measure frequency. It can also be used for the instrument of an unknown capacitor with great accuracy,

The impedance of one arm is

The admittance of the parallel arm is

                                                               

Using the bridge balance equation, we have

                                                           

Therefore

                                                            ,  i.e. 

                                                           

                                                           

                                               

Equating the real and imaginary terms we have

                                                             =    and     = 0

Therefore

                                                             =  +  …………………….(1)

And

                                                   ……………….(2)

                                         

                                       

                                       2ᴨf

So

                                        ……………..(3)                     

Where symbols have their usual meaning as shown in figure.

The two conditions for bridge balance, result in an expression determining the required resistance ratio / and another express determining the frequency of the applied voltage. If we satisfy Eq. (1) an also excite the bridge with the frequency of Eq. (3), the bridge will be balanced. In most Wien bridge circuits, the components are chosen such that = = R and  =  = C. Equation (1) therefore reduces to /=2 at Eq. (3) to f= 1/2ПRC, which is the general equation for the frequency of  bridge circuit. The bridge is used for measuring frequency in the audio range. Resistances and  can be ganged together to have identical values. Capacitors  and C3 are normally of fixed values.

The audio range is normally divided into 20 - 200 - 2 k - 20 kHz range In this case, the resistances can be used for range changing and capacitors, and  for fine frequency control within the range. The bridge can also be use for measuring capacitances. In that case, the frequency of operation must be known. The bridge is also used in a harmonic distortion analyzer, as a Notch filter, an in audio frequency and radio frequency oscillators as a frequency determine element. An accuracy of 0.5% - 1% can be readily obtained using this bridge. Because it is frequency sensitive, it is difficult to balance unless the waveform of the applied voltage is purely sinusoidal.

Circuit Diagram:-

 

Fig.10.1 : Wein’s Bridge

Procedure:-

  1. Make connections as shown in fig. i.e. connect source point with AC source, connect Headphone at detector point  in your given kit.
  2. Now select capacitor  and  value.
  3. Now vary  and  for balancing the circuit, so that no sound is heard in Headphone. This is known as AC balancing. Note the value of  and .
  4. Calculate the value of frequency using above formula and given value of  &   for your circuit.
  5. Repeat the Points 1 to 4 for the different sources.

Observations:-

  1. = ……….Ω
  2.  =………..Ω
  3.  Table for value of  and   

 

Sr. No.

Capacitor

 

(µf)

Capacitor

 

(µf)

 (Ω)

 (Ω)

f(Hz)

(Frequency)

1

 

 

 

 

 =

2

 

 

 

 

 =

3

 

 

 

 

  =

Calculation:

Show calculation for all value of frequencies (f).

Result:

  1. Frequency of source I is   = …..….Hz
  2. Frequency of source II is  = …..….Hz
  3. Frequency of source III is = …..….Hz

Precaution:

  1. Connection should be proper way.
  2. Don’t temper with equipment if there is no response in measurement.
  3. Measurement should be in a specific range of frequency.
  4. Switch of the supply of system when not in use.

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