lecture 5 electrical bridges

8/10/2019 Lecture 5 Electrical Bridges

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Pharos University

EE212_ELECTRICAL MEASUREMENT & Interface

Prepared By:Dr. Sahar Abd El Moneim Moussa

Dr. Sahar Abd El Moneim Moussa 1


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CH5_ BRIDGES


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PART (1): DC BRIDGES


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Bridges

Bridges are circuits used to measure unknown resistance,inductance and capacitance values.Bridges are classified either as DC bridges or AC bridgesdepending on the electric power supply.



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1- DC Bridges

Wheatstone Bridge:A- Balance Condition:

Wheatstone bridge is used to measure the unknown valueof the resistance of a wire between 1 to the low mega

Ohm range.Where:R1: is a fixed known resistanceR2: is a fixed known resistanceR3: is a variable resistanceR x :is the unknown resistance

Galvanometer (G), is connected between terminals D and B.Dr. Sahar Abd El Moneim Moussa 5


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The bridge is said to be at balance when the null detector(galvanometer) reads zero current, (null).This condition is reached by varying the variable resistance(R3) until the galvanometer reads zero current which meansthe potential of terminal B equals the potential of terminalD.Balance condition;

VAB = VAD I1R1=I2R2 VDC = VBC I3R3=I4Rx VD = VB I1=I3 & I2=I4 Dividing (1) and (2), then substituting with (3) we get,


=

(1) (2) (3)


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Example (1):A Wheatstone bridge has a ratio arm of 1/100 (R2/R1). At firstbalance, R3 is adjusted to 1000.3 . The value of Rx is thenchanged by the temperature change, the new value of R3 toachieve the balance condition again is 1002.1 . Find thechange of Rx due to the temperature change.Solution:



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B Limiting Error of the unknown resistor:IF

=

=

=

Therefore:



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Example (2):In the Wheatstone bridge circuit, R3 is a decade resistancewith a specified in accuracy 0.2% and R 1 and R 2 = 500 0.1%. If the value of R3 at the null position is 520.4 ,determine the possible minimum and maximum value of R X.Solution:



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C Sensitivity of the galvanometer:

In order to know weather this instrument is suitable todetect an unbalance condition, it is necessary to calculatethe galvanometer sensitivity.This can be achieved by introducing small unbalance for thebridge circuit and calculate the galvanometer deflection. If this deflection could be observed this galvanometer issuitable for this bridge to accurately measure the unknownresistor at true balance condition.The solution of the unbalanced Wheatstone bridge circuitmay be obtained using Thevenin's theorem.



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To determine the current through the galvanometer, thefollowing steps are performed:

1- Determine Thevenin's voltage V TH

2-Determine Thevenin's resistance R TH



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3- Find Thevenin's equivalent circuit:

4-Calculate the galvanometer current knowing its internal resistance:

Knowing the galvanometer sensitivity find the deflection.



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SPECIAL CASE:



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Example (3):Figure below show the schematic diagram of a Wheatstonebridge with values of the bridge elements. The battery voltage

is 5 V and its internal resistance negligible. The galvanometerhas a current sensitivity of 10 mm/ A and an internalresistance of 100 . Calculate the deflection of thegalvanometer caused by the 5- unbalance in arm BC-

Solution:



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Solution:



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Quality Factor & Dissipation Factor :i- Quality factor: It is the ratio between the reactance andthe resistance of a coil.

ii- Dissipation factor: It is the ratio between the reactanceand the resistance of a capacitor.



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Example (6):A Maxwells capacitance bridge shown in Fig. 1 is used to measure anunknown inductance in comparison with capacitance. The various

values at balance are:

Derive an expression of the unknownparameters R 1 and L1 at balance condition.

Calculate the values of R 1 and L1 and the limiting errors in percent.

Calculate the value of storage Q-factorof the coil if frequency is 1 kHz



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Solution:


It will Solved in the lecture

lecture 5 electrical bridges

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