THE DESIGN, CONSTRUCTION AND APPLICATION OF THE METRE BRIDGE

THE DESIGN, CONSTRUCTION AND APPLICATION OF THE METRE 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

1.0       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). 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.

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. chritle in 1833, only seven (7) years latter, 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 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.

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 . 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.

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 galvanorneter 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 galvanorneter, 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 (Pd) across R equals the P.d across 0;

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

1. 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.

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