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Bridge Circuits for the Measurement Malaya Journal of Matematik, Vol.S, No.2, 3089-3093, 2020 https://doi.org/10.26637/MJM0S20/0792 Bridge circuits for the measurement C. Mani,1 S. Ravi,2 V. Sathya Narayanan 3 and S. Aarthi Suriya 4 Abstract In this projects, a bridge circuit is a topology of electrical circuitry in which two circuit branches (usually in parallel with each other) are ”bridged” by a third branch connected between the first two branches at some intermediate point along them. Bridge circuits now find many applications, both linear and non-linear, including in instrumentation, filtering and power conversion. As we saw with DC measurement circuits, the circuit configuration known as a bridge can be a very useful way to measure unknown values of resistance. Keywords Bridge circuit. 1,2,3,4Department of Electrical and Electronics Engineering, Bharath Institute of Higher Education and Research, Chennai, Tamil Nadu, India. Article History: Received 01 October 2020; Accepted 10 December 2020 c 2020 MJM. Contents the unknown resistor and its neighbor R3, which enables the value of the unknown resistor to be calculated. The Wheat- 1 Introduction......................................3089 stone bridge has also been generalized to measure impedance 2 Types of Maxwell’s Bridge . 3089 in AC circuits, and to measure resistance, inductance, capaci- tance,and dissipation factor separately. 2.1 Maxwell’s Inductance Bridge............ 3090 2.2 Maxwell’s Inductance Capacitance Bridge.. 3090 3 Anderson Bridge.................................3090 3.1 Constructions of Anderson’s Bridge...... 3090 3.2 Phasor Diagram of Anderson’s Bridge..... 3091 4 Schering Bridge..................................3091 5 Wheatstone bridge...............................3092 5.1 Construction of Wheatstone bridge....... 3092 5.2 Working of Galvanometer.............. 3092 6 Hardware Trainer Kit.............................3093 Fig 1.1 Maxwell Bridge. 7 Conclusion.......................................3093 References.......................................3093 All are based on the same principle, which is to compare the output of two potential dividers sharing a common source. In power supply design, a bridge circuit or bridge rectifier is 1. Introduction an arrangement of diodes or similar devices used to rectify A bridge circuit is a topology of electrical circuitry in which an electric current, i.e. to convert it from an unknown or two circuit branches (usually in parallel with each other) are alternating polarity to a direct current of known polarity. In ”bridged” by a third branch connected between the first two some motor controllers, an H-bridge is used to control the branches at some intermediate point along them. The bridge direction the motor turns. was originally developed for laboratory measurement pur- poses and one of the intermediate bridging points is often 2. Types of Maxwell’s Bridge adjustable when so used. Two methods are used for determining the self-inductance of The variable resistor is adjusted until the galvanometer the circuit. They are reads zero. It is then known that the ratio between the vari- able resistor and its neighbor R1 is equal to the ratio between 1. Maxwell’s Inductance Bridge Bridge circuits for the measurement — 3090/3093 2. Maxwell’s inductance Capacitance Bridge 2.1 Maxwell’s Inductance Bridge In such type of bridges, the value of unknown resistance is determined by comparing it with the known value of the standard self-inductance. The connection diagram for the balance Maxwell Bridge is shown in the figure below. Fig 1.4 Maxwell’s Inductance Capacitance Bridge Fig 1.2 Maxwell’s Inductance Bridge Let, L1 – unknown inductance of resistance R1. Let, L - unknown inductance of resistance R . 1 1 R1 – Variable inductance of fixed resistance r1. L2 - Variable inductance of fixed resistance r1. R ;R ;R – variable resistance connected in series with R2 - variable resistance connected in series with inductor 2 3 4 inductor L . L2. 2 R3, R4 - known non-inductance resistance C4 – known non-inductance resistance At balance, The value of the R3 and the R4 resistance varies from 10 to 1000 ohms with the help of the resistance box. Sometimes for balancing the bridge, the additional resis- tance is also inserted into the circuit. The phasor diagram of Maxwell’s inductance bridge is shown in the figure below. 3. Anderson Bridge The Anderson’s bridge gives the accurate measurement of self-inductance of the circuit. The bridge is the advanced form of Maxwell’s inductance capacitance bridge. In Ander- son Bridge, the unknown inductance is compared with the standard fixed capacitance which is connected between the two arms of the bridge. Fig 1.3 Phasor diagram of Maxwell’s inductance bridge. 3.1 Constructions of Anderson’s Bridge 2.2 Maxwell’s Inductance Capacitance Bridge In this type of bridges, the unknown resistance is measured The bridge has fours arms ab, bc, cd, and ad. The arm ab con- with the help of the standard variable capacitance. The con- sists unknown inductance along with the resistance. And the nection diagram of the Maxwell Bridge is shown in the figure other three arms consist the purely resistive arms connected below. in series with the circuit. 3090 Bridge circuits for the measurement — 3091/3093 capacitor bushing, insulating oil and other insulating materials. It is one of the most commonly used AC Bridge. Fig 1.7 Schering Bridge Fig 1.5 Anderson’s Bridge The static capacitor and the variable resistor are connected Let, C1 – capacitor whose capacitance is to be determined in series and placed in parallel with the cd arm. The voltage r1 – a series resistance, representing the loss of the capaci- source is applied to the terminal a and c. tor C1. C2 – a standard capacitor (The term standard capacitor 3.2 Phasor Diagram of Anderson’s Bridge means the capacitor is freefromloss) The phasor diagram of the Anderson Bridge is shown in the R3 –anon-inductiveresistance figure below. The current I1 and the E3 are in phase and represented on the horizontal axis. When the bridge is in C4 –avariablecapacitor. balance condition the voltage across the arm bc and ecare R4 – a variable non-inductive resistance parallel with vari- equal. able capacitor C4. When the bridge is in the balanced condition, zero current passes through the detector, which shows that the potential across the detector is zero. At balance condition Z1=Z2 = Z3=Z4 Z1Z4 = Z2Z3 So,Equating the real and imaginary equations, we get Fig 1.6 Phasor Diagram of Anderson’s Bridge The current enters into the bridge is divided into the two parts R3C4 r1 = (4.1) I1 and I2. The I1 is entered into the arm ab and causes the C2 voltage drop I1(R1 + R) which is in phase with the I1. As the bridge is in the balanced condition, the same current is passed through the arms bc and ec.The voltage drop E4 is equal to R4 the sum of the IC=wC and the ICr. The sum of the current IC C1 = C2 (4.2) R3 and I4 will give rise to the current I2 in the arm ad. When the bridge is at balance condition the emf across the arm ab and the point a, d and e are equal. The equation (4.1) and (4.2) are the balanced equation, and it is free from the frequency. 4. Schering Bridge The dissipation factor obtains with the help of the phasor diagram. The dissipation factor determines the rate of loss of The Schering bridge use for measuring the capacitance of energy that occurs because of the oscillations of the electrical the capacitor, dissipation factor, properties of an insulator, and mechanical instrument. 3091 Bridge circuits for the measurement — 3092/3093 Fig 1.8 Phasor diagram of low voltage Schering Bridge Fig 1.9 Wheatstone bridge The EMF supply is attached between point a and b, and the galvanometer is connected between point c and d. The current through the galvanometer depends on the potential difference across it. D1 = tand = wC1r1 = w (C1r1) = w (C2R4=R3) × (R3C4=C2) D1 = wC4R4 5.2 Working of Galvanometer The bridge is in balance condition when no current flows through the coil or the potential difference across the gal- By the help of the above equation, we can calculate the value vanometer is zero. This condition occurs when the potential of tand which is the dissipation factor of the Schering Bridge. difference across the a to b and a to d are equal, and the potential differences across the b to c and c to d remain same. The current enters into the galvanometer divides into I1 and I2, and their magnitude remains same. The following condition exists when the current through the galvanometer is 5. Wheatstone bridge zero. The device uses for the measurement of minimum resistance I1P = I2R (5.1) with the help of comparison method is known as the Wheat- The bridge in a balanced condition is expressed as stone bridge. The value of unknown resistance is determined E by comparing it with the known resistance. The Wheatstone I1 = I3 = P+Q E bridge works on the principle of null deflection, i.e. the ratio I2 = I4 = R+S of their resistances are equal, and no current flows through Where E – EMF of the battery. the galvanometer. The bridge is very reliable and gives an By substituting the value of I and I in equation (5.1) we accurate result. 1 2 get. In normal condition, the bridge remains in the unbalanced PE RE = condition, i.e. the current flow through the galvanometer. P + Q R + S When zero current passes through the galvanometer, then P R the bridge is said to be in balanced condition. This can be = P + Q R + S done by adjusting the known resistance P, Q and the variable resistance S.
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