لخّصلي

Theory: In this bridge one of the arms (AB) contains a variable standard capacitor C connected in series with a variable standard resistor as shown in Figure (2).Figure(2): Wien's bridge The two arms BC and CD contain two pure ohmic resistors R1 and R2 respectively, these should be of the same order or may be made equal.It is important to record the frequency of oscillation at which the measurements are made, since both the capacity and the resistance are dependent on the frequency.The bridge is used to measure the capacity of a capacitor and the resistance which are placed in the remaining arm.The resistor r is adjusted until silence is obtained as nearly as possible.The bridge is most sensitive when all the arms are equal.

Theory:
In this bridge one of the arms (AB) contains a variable standard capacitor
C connected in series with a variable standard resistor as shown in Figure (2).
Figure(2): Wien's bridge
The two arms BC and CD contain two pure ohmic resistors R1 and R2
respectively, these should be of the same order or may be made equal. The bridge
is used to measure the capacity of a capacitor and the resistance which are placed
in the remaining arm. An ear phone is placed in the arm BD and is used to detect
the condition of balance; the condition of balance of the bridge occurs when there
is silence in the ear phone which means that no current passes from B to D in other
words there is no potential difference between B and D, thus at balance the
potential difference between A & B equals to that between A & D and therefore:
i1 ( r + 1/jωC ) = i2 ( r1+ 1/jωC1 ) ( 2 )
Similarly
i1 ( R1 ) = i2 ( R2 ) ( 3 )
Eliminating i1 and i2 by dividing Eq. ( 2 ) by Eq. ( 3 ) we get
( r + 1/jωC ) / R1 = ( r1 + 1/jωC1 ) / R2
Thus
r1R1 + R1 ( 1/jωC1 ) = R2 r + R2 ) 1/jωC ) (5)
Equating the real parts we get:
r1 = r R2 / R1 (6)
And equating the imaginary parts we obtain:
C1 = C R1 / R2 (7)
In practice the condition of balance is obtained by adjusting the capacitor
until a minimum sound is heard in the phone. The resistor r is adjusted until
silence is obtained as nearly as possible.
The bridge is most sensitive when all the arms are equal. It is important
to record the frequency of oscillation at which the measurements are made, since
both the capacity and the resistance are dependent on the frequency.