The Schering Bridge

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The Wien Bridge

• As shown in Figure, one arm of a Wien bridge consists of a capacitor in series with a resistor (C1 and R3) and another arm consists of a capacitor in parallel to a resistor (C2 and R4).
• The other two arms simply contain a resistor each (R1 and R2).
• The values of R1and R2 are known, and R4 and C2 are both adjustable.
• The unknown values are those of C1 and R3.

 

• Like other bridge circuits, the measuring ability of a Wien Bridge depends on 'balancing' the circuit.
• Balancing the circuit in Figure means adjusting R4 and C2 until the current through the ammeter between points A and B becomes zero.
• This happens when the voltages at points A and B are equal.
• When the Wien Bridge is balanced, it follows that R2/R1 = Z1/Z2 where Z1 is the impedance of the arm containing C1 and Z2 is the impedance of the arm containing C2.

 

• Mathematically, when the bridge is balanced,  

R2/R1 = (1/ωC1 + R3) / (R4/[ωC2(R4 + 1/ωC2)]) wherein ω = 2πf; or 
R2/R1 = (1/ωC1 + R3) / (R4/[ωC2R4 + 1]); or 
R2/R1 = (1/ωC1 + R3) (ωC2 + 1/R4); or 
R2/R1 = C2/C1 + ωC2R3 + 1/(ωC1R4) + R3/R4.

• When the bridge is balanced, the capacitive reactances cancel each other out, so   

R2/R1 = C2/C1 + R3/R4. Thus, C2/C1 = R2/R1 - R3/R4.

 

• Note that the balancing of a Wien Bridge is frequency-dependent. 
• The frequency f at which the Wien Bridge in Figure becomes balanced is the frequency at which ωC2R3 = 1/(ωC1R4), or 2πfC2R3 = 1/(2πfC1R4). 
• Thus, the frequency f is given by the following equation:  f = (1 / 2π) x (sqrt(1/[R3R4C1C2])).

The Wien Bridge

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The Wheatstone Bridge

• In the Wheatstone Bridge shown in Figure, the resistance values of resistors R2, and R3 are known, while the resistance value of variable resistor R1 may be adjusted

 

• The resistance value of R1 is adjusted until the current reading of the ammeter connected between points A and B of the circuit becomes zero.
• When this happens, the bridge is said to be 'balanced', i.e., the voltages at points A and B are already equal, so the value of the unknown resistance may easily be calculated using voltage ratios:  

 Runknown / R3 = R1 / R2.  

 

• The equivalent resistance Rb of the circuit when it is balanced is just the resistance of the left leg (R1+R2) in parallel with the resistance of the right leg (R3+Runknown).
      
  Rb = [(R1+R2)(R3+Runknown)] / [R1 + R2 + R3 + Runknown].

   

  Alternatively, if the resistance values of R1, R2, and R3 are known but R1can not be adjusted, then the value of Runknown can still be calculated using Kirchhoff's Voltage Law.

   

  This set-up is often seen in strain gauges and resistance temperature detection circuits, since it is quicker to read a voltmeter than to manually adjust a resistor to balance the circuit.