AC B RIDGES AC bridge and their application : Head phone ~ I2I2 I1I1 Z2Z2 Z1Z1 Z4Z4 Z3Z3

B ALANCE C ONDITION The condition for bridge balance requires that the potential difference from A to C to be zero. This will be the case when the voltage drop from B to A equals the voltage drop from B to C in both magnitude and phase. So at balance : I 1 Z 1 = I 2 Z 2 But

B ALANCE C ONDITION ( CONT.) But Equation (1) can be written in the form:

B ALANCE C ONDITIONS ( CONT.)

E XAMPLE EX. The impedance of the AC bridge are given by: Determine Z 4

E XAMPLE ( CONT.) Solution: The 1 st condition of balance

E XAMPLE ( CONT.) The 2 nd condition of balance Indicating that we are dealing with a capacitive element possibly consisting of a series resistor and a capacitor.

M AXWELL B RIDGE The Maxwell Bridge measures an unknown inductance in terms of a known standard capacitance. indicator E R1 RxRx R2 R3 C1 LxLx

M AXWELL B RIDGE ( CONT.)

Note: --- For getting balance : R 3 for inductive balance and R 1 for resistance balance The Maxell bridge is limited to the measurement of medium quality factor Q (1<Q<10 ). The quality factor Q is defined by :

M AXWELL B RIDGE ( CONT.) For the Maxwell bridge, the second condition of balance is: Thus for the case of high Q (Q>10) of the coil θ 4 will be nearly 90. ( θ 4 = tan -1 (ωL x /R x ) which requires that the phase angle of the capacitive arm to be nearly – 90 and this can be satisfied for very large value of R 1 which can be impractical as shown from the following discussions :

M AXWELL B RIDGE ( CONT.) R 1 must be very large which may be practically impossible. because f ≈ 50 Hz, C ≈ 1nF R 1 must be great. For coils of high quality Hay bridge is used where parallel R 1 & C 1 circut are displaced by series R 1 & C 1 circuit

W EIN B RIDGE The Wien Bridge is used for measuring the frequency of the voltage source E indicator R1 R2 R3 R4 C3 C1 E Indicator

W EIN B RIDGE ( CONT.) Condition of balance:

W EN B RIDGE ( CONT.) if R 1 = R 3 = R & C 1 = C 3 = C In practical circuit bridge, capacitors C 1, C 3 are fixed capacitors and resistors R 1, R 3 are variable resistors controlled by a common shaft providing also R 2 = 2 R 4.

D’A RSONVAL METER MOVEMENT USED WITH FULL - WAVE RECTIFIER Rs I p (peak value) I rms t I V av

D’A RSONVAL METER MOVEMENT USED WITH FULL - WAVE RECTIFIER I rms = 0.7 I p I dc = 2/π I p I dc = I av = 0.9 I rms Form factor = 1/0.9 = 1.11.

E XAMPLE EX: For the circuit shown in Fig. Each diode has forward resistance of 50Ω and is assumed to have an infinite resistance in the reverse direction. Calculate the following: The value of the multiplier R s. The ac sensitivity S ac. The dc sensitivity S dc. RsRs I fsd = 1mA R m = 100 Ω E = 10 v

E XAMPLE ( CONT.) (a) The equivalent dc voltage V dc = V av = 0.9 X 10 = 9 v R T = 2R D + R s + R m = 9/I fsd = 9/0.001 = 9000 R s = R T – 2 R D – R m = 9000 – 2 X 50 – 100 =8800 Ω (b) R T = S av. V S av = 9000/10 = 900 Ω/v (c) S av = 0.9 S dc = 1/ I fsd S dc = 900/ 0.9 = 1000 Ω/v = 1/0.001=1000 Ω/v