DESIGN, CONSTRUCTION AND APPLICATION OF METER BRIDGE

DESIGN, CONSTRUCTION AND APPLICATION OF METER BRIDGE

ABSTRACT

Wheatstone bridge has long been used in electronic measurement, and it is the most accurate method employed for measuring resistance of materials. Recent studies have also established the practical arrangement of Wheatstone bridge (Meter Bridge) for resistance measurement. This write up is solely concerned with the construction of Meter Bridge using copper and its application as well as testing it using the constructed meter bridge.

CHAPTER ONE

INTRODUCTION

Electrical and electronic measurements embrace all the devices and systems that utilize electrical and electronic phenomena in the operation to ascertain the dimension, state, quantity or capacity of an unknown by comparing it with a fixed known or reference quantity. The unknown quantity being determined is commonly referred to as the measured or the standard which may or may not be an electrical quantity but it must be appreciated that electrical quantities are ultimately determined in terms of the primary standard of length, mass and temperature.

Within the definition of electrical measurement it has been noted that the magnitude of the measure (or unknown) is ascertained by comparing it with a reference quantity. It is necessary, therefore, in practice, to have in every measuring instrument or system a known or reference quantity that may or may not have the same units as the measured an unknown resistor, for example, while a current may be compared with a force (spring) or voltage (IR drop) Abbot, and Nelkon, (1971). Hence, in measuring, electrical quantities, various techniques which are identifiable have evolved as well as the need for reference or standard values and for a means of establishing how remote the measured value may form the standard.

1.1       WHEAT STONE BRIDGE

A device used to measure the electrical resistance of an unknown resistor by comparison with a known standard resistance. This method was first described by S.H. Christie in 1833, only seven (7) years later, George S. Ohm discovered the relationship between voltage and current. Since, 1843 that Sir Charles wheat stone drew attention to Christie’s work. The wheat stone bridge network has consisted of four resistor; RAB, RBC, RCD and RAD, interconnected as shown in fig (1) (wheat stone bridge circuit) to form the bridge.

A current G, having an internal resistance RG. Is connected between the B and D bridge points; and a power supply having an open circuit voltage E, and internal resistance RB, is connected between A and C, bridge points

Application of ohm’s and Kurchnoff’s law to the network result in the equation below:

IG = I_B (R_BC R­_AD – R_ABR_CD) ………………………………………. Eqn. (i)

            R_G (R_AB + R_BC + R_CD + R­_AD) + (R_BC + R_CD + R_AB + R­_AD)

For the detector current in this expression

I_B =                              E                      ……..……………………………..eqn. (ii)

R_G (R_AB + R_BC + R_CD + R­_AD)

R_AB + R_BC + R_CD + R­_AD

It is apparent from equation (1), that, if the network is adjusted so that

R_BC R­_AD – R_AM R_CD = 0 ………………………………eqn. (iii). The detector current will be zero and this adjustment will be independent of the supply voltage, the resistance and the detector resistance. Thus, when bridge is balanced;

R_BC R­_AD – R_AB R_CD ……………………………………………………….eqn. (iv)

And if it is assured that the unknown resistance is the one in the CD arm of the bridge then, R_CD = R_BC /R­_AB X R­_AD …………………………………………….eqn. (v)

Three methods of adjustment to achieve this condition are possible when the current is used as a ratio arm bridge:

1. Use of a fixed ratio R_BC /R­_AB and a continuously adjustable standard R­_AD
2. Use of a continuously adjustable ratio and a fixed standard.
3. A combination of the foregoing with the ratio usually adjustable in discrete steps of decade values.

The first method provides a linear calculation of known varying standard resistance, but is limited in resistance range to the adjustable from zero to infinity, but results in a non linear scale, highly expanded for higher resistance standard of three to five decades wide range and linear calibration and of the most practice of the combination for general use with reasonable accuracy. If the current is considered as a product arm bridge, it is observed that conductance G_CD of unknown resistance

Red = R_BC R­_AD /R_{AB ………………………………………………………………………………………..}eqn. (vi)

SENSITIVITY: The sensitivity of the bridge assembly battery, bridge and detector is of two important purposes:

1. For determining the required detector sensitivity for a given deviation in the unknown resistance.
2. For determining the change in resistance which can be measured using a detector of a stated sensitivity. The precision of the balance is affected by the detector sensitivity, the detector resistance, which except for special cases can be neglected. If the detector open circuit voltage between point B and D is e EBC-ECD or e =E (R_AC R­_BC – ∆R_CD)/R_CB-∆R_CD + R­_AD ………………………eqn. (viii) where ∆R_CD) is a small incremental change in the unknown resistance R(J). This open circuit voltage due to a small bridge unknown balance, to a close approximation, can be hence, the fractional change in the unknown resistance and the applied voltage is e = E[r/(r+1)²  (R_CD/R_CD ) ………………..(ix) where r = RB_C/R_AB.

If the detector circuit is closed, current flows through the detector, the Battery resistance being regulated, this current can be calculated from Theremins theorems, IG

                        e                     

(R_ABR_BC)(R_CDR­_AD)

(R_AB + R_BC)(R_CD + R­_AD)

And in terms of unbalance arrest permit volt applies to the bridge.

The unbalanced current can thus be expressed in terms of:

1. The Fractional Change In Unknown Resistance
2. An effective detector resistance which depends upon the bridge ratio in use.
3. The sun of all the bridge resistors.
4. The applied voltage.

ACCURACY

The errors that occur in a wheat stone bridge measurement are due to:

1. The value of unknown resistance and the conditions of measurement.
2. The ability to balance the bridge to the required precession.
3. The available bridge sensitivity.
4. The errors of the comparison of resistors ratios or both.
5. An accumulation of small errors resulting from practical circuit and construction problems.

Once the allowable errors of measurement have been determined, the ability to physically adjust the bridge and the detector sensitivity are in the proportion 1:1/2:1/4, for allowable error of ≠0.05%, and the detector should be sufficiently sensitive to detect at least ≠0.0025% deviation in the measurement.

If the ratio resistors have been adjusted to their individual units of error, the error on the ratio will probably be larger than error of each resistor. For this effect, the adjustment of the bridge ratio arms often for a specified error in ratio, maintaining only a normal resistance value.

1.2       MEASUREMENT METHODS.

Since all measurements with a require comparison of the measured with a reference quantity the method by which the comparison is made will vary according to para under consideration, Its magnitude and the condition prevalent at the time of observation. The method used in electrical and electronic measurement can be categorized in to substitution and temperature coefficient (Beney, 1986).

1.2.1    SUBSTITUTION:

As the name implies, this method requires such magnitude that condition are rested, to a reference condition. For example, considering the situation illustrated in fig (iii), voltage source causes a current to flows through a circuit consisting of an am in services with an unknown resistance Rx. If the switch is changed so that the unknown is replaced by a decade resistance box Rs, the magnitudes of the decades can be objected unknown the current is restored to the value that was present when Rx was in current. The setting of Rx then becomes equal to the value of Rx. This process is only occasionally a satisfactory method of measuring a resistor, hut, in the Q . Coulson, and Boyo, (1982) A process is used for the measurement of small capacitance value, reference conditions being restored by reducing a known variable capacitor by an amount equal to the unknown capacitor.

1.2.2    TEMPERATURE COEFFICIENT OF RESISTANCE

The resistance of a given wire increases with its temperature. If a coil of fine copper wire is put into water bath, and a Wheatstone bridge used to measure temperature T, it will be found that the resistance R, increases uniformly with temperature.

The temperature coefficient of resistance is given by; R=Ro (1+t) ……eqn. (xi) where, Ro the resistance at 0°c in wood =

Increase in resistance per degree (rise in temp.)

Resistance at 0°C.

If R₁ and R₂ are the resistance at T₁0C and T₂0C,

Then R₁/ R₂ = 1+t₁/R+vt₂ ………………………………………………..eqn. (xii)

Value for pure metals is of the order of 0.004 per degree Celsius. They are much less than impure metals, a fact which enhances the value of alloy materials for resistances boxes and shunts.

1.3       THE METRE BRIDGE

A bridge composes of a straight uniform resistance wire AB, one  long stretched over a box wood scale graduated in millis and mounted on a board. The ends of the wire arc clamped to shout copper or brass strips A and C and a third and longer strip B, is screwed to the board parallel to the wire terminals are provided on the strip for making the necessary connections and movable contact or jockey which enables contact to be made at any point along the wire. Gewish, (1974).

The practical circuit shown in fig (v) shows the unknown resistance connected to the gap between strips A and B and a standard resistance B and C, a sensitive centre zero galvano is inserted between B and the contact on the wire at‘d’. A cell and a tapping key are connect a cross AC.

The resistance box s, first adjusted to the value of R. the battery key is the pressed and after ward contact with the jockey is made at various points along the bridge wire until a point is researched for which the galvanometer provides null deflection the two resistances P and Q are formed by the two lengths of the bridge wire L1 and L2 in the practical circuit. Since the resistance will be proportional to the length of the wire and thus. P/Q =  L₁/L₂ ………………………………….eqn. (xiii)

Hence, instead of using R = SP/Q ………………….eqn. (xiv)

Suppose the current entering the network at ‘A’ divides up into LI through P, if no current flows through galvanometer, the current through S and Q must be equal to LI and 12 respectively. Also if since current flows, through the galvano, the potentials of B and D must be equal. Hence for a balance or null deflection of the galvano;

Potential difference (P.d) across R equals the P.d across 0;

Potential difference (P.d) across S equals the Rd across Q, and

P. d = current x resistance or since, L₁R = L₂P …………….eqn. (xvi)

And L₁S = L₂Q ……………………………………………..eqn. (xvii)

Dividing equation (xvi) b equation (x vii) L1R/L1S = L2P/L2Q.

Hence, R/S P/ Q

I.e. the unknown resistance R = S x P / Q. Since only the radio of P and Q is, however, required to calculate R, whetstone found it rather more convenient to replace P and Q by a uniform resistance which could be divided in to two parts by a movable contact the . This principle is used in the  bridge form of the Wheatstone bridge.